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Arkiv for Matematik, 2012, Volume 51
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (19 articles)
Issue 1
[1] Noise correlation bounds for uniform low degree functions
Per Austrin Department of Computer Science, University of Toronto Elchanan Mossel University of California, Berkeley, 367 Evans Hall, Berkeley, CA, U.S.A.
Combinatorics Optimization and Control mathscidoc:1701.06003
Arkiv for Matematik, 51, (1), 29-52, 2010.8
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We study correlation bounds under pairwise independent distributions for functions with no large Fourier coefficients. Functions in which all Fourier coefficients are bounded by$δ$are called$δ$-$uniform$. The search for such bounds is motivated by their potential applicability to hardness of approximation, derandomization, and additive combinatorics.
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[2] Volume formula for a ℤ_{2}-symmetric spherical tetrahedron through its edge lengths
Alexander Kolpakov Departement für Mathematik, Universität Freiburg Alexander Mednykh Sobolev Institute of Mathematics, Novosibirsk State University Marina Pashkevich Department of Mathematics and Mechanics, Novosibirsk State University
Symplectic Geometry mathscidoc:1701.34001
Arkiv for Matematik, 51, (1), 99-123, 2010.8
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Murakami J. The volume formulas for a spherical tetrahedron[J]. Proceedings of the American Mathematical Society, 2010, 140(9): 3289-3295.
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Ivanova I A, Leydesdorff L. Knowledge-generating efficiency in innovation systems: The acceleration of technological paradigm changes with increasing complexity[J]. Technological Forecasting and Social Change, 2015, 96(1): 254-265.
3
Kolpakov A A. On extremal properties of hyperbolic Coxeter polytopes and their reflection groups[C]., 2012.
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Kolpakov A, Murakami J. Volume of a doubly truncated hyperbolic tetrahedron[J]. Aequationes Mathematicae, 2012, 85(3): 449-463.
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Petrera M, Suris Y B. Spherical geometry and integrable systems[J]. Geometriae Dedicata, 2012, 169(1): 83-98.
6
Alexander Kolpakov · Jun Murakami. The dual Jacobian of a generalised tetrahedron, and volumes of prisms. 2014.
Abstract
The present paper considers volume formulæ, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation of angle$π$in the middle points of a certain pair of its skew edges.
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[3] Asymptotic porosity of planar harmonic measure
Jacek Graczyk Department of Mathematics, University of Paris XI Grzegorz Świa̧tek Department of Mathematics and Information Sciences, Warsaw University of Technology
Classical Analysis and ODEs mathscidoc:1701.05004
Arkiv for Matematik, 51, (1), 53-69, 2010.9
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We study the distribution of harmonic measure on connected Julia sets of unicritical polynomials. Harmonic measure on a full compact set in ℂ is always concentrated on a set which is porous for a positive density of scales. We prove that there is a topologically generic set $\mathcal{A}$ in the boundary of the Mandelbrot set such that for every $c\in \mathcal{A}$ ,$β$>0, and$λ$∈(0,1), the corresponding Julia set is a full compact set with harmonic measure concentrated on a set which is not$β$-porous in scale$λ$^{$n$}for$n$from a set with positive density amongst natural numbers.
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[4] Simplicity of eigenvalues in Anderson-type models
Sergey Naboko Department of Mathematical Physics, Institute of Physics, St. Petersburg State University Roger Nichols Department of Mathematics, University of Missouri Günter Stolz Department of Mathematics, University of Alabama at Birmingham
mathscidoc:1701.02006
Arkiv for Matematik, 51, (1), 157-183, 2010.10
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Peter D Hislop · M Krishna. Eigenvalue Statistics for Random Schrödinger Operators with Non Rank One Perturbations. 2014.
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Fritz Gesztesy · Sergey Naboko · Roger Nichols. On a problem in eigenvalue perturbation theory. 2014.
3
Anish Mallick. Jakšić-Last theorem for higher rank perturbations: Jakšić-Last theorem for higher rank perturbations. 2016.
Abstract
We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schrödinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not restricted to the localization regime. We establish general criteria for the simplicity of eigenvalues which can be interpreted as separately excluding the absence of local and global symmetries, respectively. The criteria are applied to Anderson models with matrix-valued potential as well as with single-site potentials supported on a finite box.
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[5] Calculation of local formal Fourier transforms
Adam Graham-Squire Department of Mathematics, High Point University
Spectral Theory and Operator Algebra mathscidoc:1701.01017
Arkiv for Matematik, 51, (1), 71-84, 2011.2
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[6] A new generalization of the Lelong number
Aron Lagerberg Department of Mathematics, Chalmers University of Technology and University of Göteborg
Complex Variables and Complex Analysis mathscidoc:1701.08009
Arkiv for Matematik, 51, (1), 125-156, 2010.8
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We will introduce a quantity which measures the singularity of a plurisubharmonic function$φ$relative to another plurisubharmonic function$ψ$, at a point$a$. We denote this quantity by$ν$_{$a$,$ψ$}($φ$). It can be seen as a generalization of the classical Lelong number in a natural way: if$ψ$=($n$−1)log| ⋅ −$a$|, where$n$is the dimension of the set where$φ$is defined, then$ν$_{$a$,$ψ$}($φ$) coincides with the classical Lelong number of$φ$at the point$a$. The main theorem of this article says that the upper level sets of our generalized Lelong number, i.e. the sets of the form {$z$:$ν$_{$z$,$ψ$}($φ$)≥$c$} where$c$>0, are in fact analytic sets, provided that the$weight$$ψ$satisfies some additional conditions.
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[7] On the$h$-triangles of sequentially ($S$_{$r$}) simplicial complexes via algebraic shifting
Mohammad Reza Pournaki Department of Mathematical Sciences, Sharif University of Technology Seyed Amin Seyed Fakhari Department of Mathematical Sciences, Sharif University of Technology Siamak Yassemi School of Mathematics, Statistics and Computer Science College of Science, University of Tehran
mathscidoc:1701.01018
Arkiv for Matematik, 51, (1), 185-196, 2011.3
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Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially ($S$_{$r$}) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen–Macaulay and satisfying Serre’s condition ($S$_{$r$}). Let Δ be a ($d$−1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let ($h$_{$i$,$j$}(Δ))_{0≤$j$≤$i$≤$d$}be the$h$-triangle of Δ and ($h$_{$i$,$j$}(Γ(Δ)))_{0≤$j$≤$i$≤$d$}be the$h$-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially ($S$_{$r$}) and for every$i$and$j$with 0≤$j$≤$i$≤$r$−1, the equality$h$_{$i$,$j$}(Δ)=$h$_{$i$,$j$}(Γ(Δ)) holds true.
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[8] Verdier specialization via weak factorization
Paolo Aluffi Mathematics Department, Florida State University
K-Theory and Homology mathscidoc:1701.01019
Arkiv for Matematik, 51, (1), 1-28, 2010.10
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Let$X$⊂$V$be a closed embedding, with$V$∖$X$nonsingular. We define a constructible function$ψ$_{$X$,$V$}on$X$, agreeing with Verdier’s specialization of the constant function$1$_{$V$}when$X$is the zero-locus of a function on$V$. Our definition is given in terms of an embedded resolution of$X$; the independence of the choice of resolution is obtained as a consequence of the weak factorization theorem of Abramovich–Karu–Matsuki–Włodarczyk. The main property of$ψ$_{$X$,$V$}is a compatibility with the specialization of the Chern class of the complement$V$∖$X$. With the definition adopted here, this is an easy consequence of standard intersection theory. It recovers Verdier’s result when$X$is the zero-locus of a function on$V$.
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[9] Area-preserving isotopies of self-transverse immersions of$S$^{1}in ℝ^{2}
Cecilia Karlsson Department of Mathematics, Uppsala University
Metric Geometry Symplectic Geometry mathscidoc:1701.23001
Arkiv for Matematik, 51, (1), 85-97, 2011.3
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Let$C$and$C$′ be two smooth self-transverse immersions of$S$^{1}into ℝ^{2}. Both$C$and$C$′ subdivide the plane into a number of disks and one unbounded component. An isotopy of the plane which takes$C$to$C$′ induces a one-to-one correspondence between the disks of$C$and$C$′. An obvious necessary condition for there to exist an area-preserving isotopy of the plane taking$C$to$C$′ is that there exists an isotopy for which the area of every disk of$C$equals that of the corresponding disk of$C$′. In this paper we show that this is also a sufficient condition.
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Issue 2
[1] Möbius homogeneous hypersurfaces with two distinct principal curvatures in$S$^{$n$+1}
Tongzhu Li Department of Mathematics, Beijing Institute of Technology Xiang Ma LMAM, School of Mathematical Sciences, Peking University Changping Wang LMAM, School of Mathematical Sciences, Peking University
Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1701.10010
Arkiv for Matematik, 51, (2), 315-328, 2011.4
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[2] An extension property of the Bourgain–Pisier construction
Jesús Suárez de la Fuente Department Mathematics, Escuela Politécnica
Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12023
Arkiv for Matematik, 51, (2), 363-369, 2011.4
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[3] On the Carleson duality
Tuomas Hytönen Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströms gata 2b), Helsingfors universitet, Finland Andreas Rosén Department of Mathematics, Linköpings universitet
Analysis of PDEs mathscidoc:1701.03025
Arkiv for Matematik, 51, (2), 293-313, 2011.4
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Auscher P, Rosen A. Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II[J]. Analysis \u0026 PDE, 2010, 5(5): 983-1061.
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Hofmann S, Kenig C E, Mayboroda S, et al. The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients[J]. Mathematische Annalen, 2013: 863-907.
3
Rosen A. Cauchy non-integral formulas[C]., 2012: 163-178.
4
Pascal Auscher · Dorothee Frey. ON THE WELL-POSEDNESS OF PARABOLIC EQUATIONS OF NAVIER–STOKES TYPE WITH DATA. 2015.
Abstract
As a tool for solving the Neumann problem for divergence-form equations, Kenig and Pipher introduced the space ${\mathcal{X}}$ of functions on the half-space, such that the non-tangential maximal function of their$L$_{2}Whitney averages belongs to$L$_{2}on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of ${\mathcal{X}}$ , and characterize the pointwise multipliers from ${\mathcal{X}}$ to$L$_{2}on the half-space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to$L$_{$p$}generalizations of the space ${\mathcal{X}}$ . Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.
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[4] An improved Riemann mapping theorem and complexity in potential theory
Steven R. Bell Mathematics Department, Purdue University
Complex Variables and Complex Analysis mathscidoc:1701.08010
Arkiv for Matematik, 51, (2), 223-249, 2011.10
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Bell S R, Ferguson T, Lundberg E, et al. Self-commutators of Toeplitz operators and isoperimetric inequalities[J]. Mathematical Proceedings of The Royal Irish Academy, 2012, 114(2): 1-18.
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Bell S R. The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains[C]., 2013, 5(2): 113-135.
Abstract
We discuss applications of an improvement on the Riemann mapping theorem which replaces the unit disc by another “double quadrature domain,” i.e., a domain that is a quadrature domain with respect to both area and boundary arc length measure. Unlike the classic Riemann mapping theorem, the improved theorem allows the original domain to be finitely connected, and if the original domain has nice boundary, the biholomorphic map can be taken to be close to the identity, and consequently, the double quadrature domain is close to the original domain. We explore some of the parallels between this new theorem and the classic theorem, and some of the similarities between the unit disc and the double quadrature domains that arise here. The new results shed light on the complexity of many of the objects of potential theory in multiply connected domains.
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[5] Biharmonic PNMC submanifolds in spheres
Adina Balmuş Faculty of Mathematics, “Al. I. Cuza” University of Iaşi Stefano Montaldo Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari Cezar Oniciuc Faculty of Mathematics, “Al. I. Cuza” University of Iaşi
Differential Geometry mathscidoc:1701.10011
Arkiv for Matematik, 51, (2), 197-221, 2011.10
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Caddeo R, Montaldo S, Oniciuc C, et al. Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor[J]. Annali di Matematica Pura ed Applicata, 2012, 193(2): 529-550.
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Luo Y. On biharmonic submanifolds in non-positively curved manifolds[J]. Journal of Geometry and Physics, 2013: 76-87.
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Montaldo S, Oniciuc C, Ratto A, et al. Proper Biconservative immersions into the Euclidean space[J]. Annali di Matematica Pura ed Applicata, 2013, 195(2): 403-422.
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Fetcu D, Oniciuc C, Rosenberg H, et al. Biharmonic Submanifolds with Parallel Mean Curvature in \\mathbb{S}^{n}\\times\\mathbb{R}[J]. Journal of Geometric Analysis, 2011, 23(4): 2158-2176.
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Fetcu D, Oniciuc C, Rosenberg H, et al. Biharmonic Submanifolds with Parallel Mean Curvature in \\mathbb{S}^{n}\\times\\mathbb{R}[J]. Journal of Geometric Analysis, 2011, 23(4): 2158-2176.
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Fetcu D, Oniciuc C, Pinheiro A L, et al. CMC biconservative surfaces in Sn×R and Hn×R[J]. Journal of Mathematical Analysis and Applications, 2015, 425(1): 588-609.
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Dorel Fetcu · Cezar Oniciuc · Ana Lucia Pinheiro. CMC biconservative surfaces in S n × R and H n × R. 2015.
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Ou Y. On f-biharmonic maps and f-biharmonic submanifolds[J]. Pacific Journal of Mathematics, 2013, 271(2): 461-477.
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Stefano Montaldo · Andrea Ratto. Biharmonic submanifolds into ellipsoids. 2013.
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Fu Y, Turgay N C. Complete classification of biconservative hypersurfaces with diagonalizable shape operator in Minkowski 4-space[J]. International Journal of Mathematics, 2015, 27(05).
Abstract
We obtain several rigidity results for biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector fields. We classify biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector fields and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector fields in $\mathbb{S}^{n}$ .
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[6] Proper holomorphic embeddings of finitely connected planar domains into ℂ^{$n$}
Irena Majcen Mathematisches Institut, Alpeneggstrasse 22, Bern, Switzerland
Differential Geometry Geometric Analysis and Geometric Topology Statistics Theory and Methods mathscidoc:1701.10012
Arkiv for Matematik, 51, (2), 329-343, 2012.1
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In this paper we consider proper holomorphic embeddings of finitely connected planar domains into ℂ^{$n$}that approximate given proper embeddings on smooth curves. As a side result we obtain a tool for approximating a $\mathcal{C}^{\infty}$ diffeomorphism on a polynomially convex set in ℂ^{$n$}by an automorphism of ℂ^{$n$}that satisfies some additional properties along a real embedded curve.
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[7] An essay on Bergman completeness
Bo-Yong Chen Department of Mathematics, Tongji University
TBD mathscidoc:1701.333179
Arkiv for Matematik, 51, (2), 269-291, 2011.4
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We give first of all a new criterion for Bergman completeness in terms of the pluricomplex Green function. Among several applications, we prove in particular that every Stein subvariety in a complex manifold admits a Bergman complete Stein neighborhood basis, which improves a theorem of Siu. Secondly, we give for hyperbolic Riemann surfaces a sufficient condition for when the Bergman and Poincaré metrics are quasi-isometric. A consequence is an equivalent characterization of uniformly perfect planar domains in terms of growth rates of the Bergman kernel and metric. Finally, we provide a noncompact Bergman complete pseudoconvex manifold without nonconstant negative plurisubharmonic functions.
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[8] Duality and distance formulas in spaces defined by means of oscillation
Karl-Mikael Perfekt Centre for Mathematical Sciences, Lund University
Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12024
Arkiv for Matematik, 51, (2), 345-361, 2011.6
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Contreras M D, Diazmadrigal S, Vukotic D, et al. Compact and weakly compact composition operators from the Bloch space into M\\\
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Karlmikael Perfekt. Articles on Potential Theory, Functional Analysis and Hankel Forms. 2013.
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Karlmikael Perfekt. Weak compactness of operators acting on o-O type spaces. 2014.
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J Wang · J Xiao. Analytic Campanato Spaces by Functionals and Operators. 2015.
Abstract
For the classical space of functions with bounded mean oscillation, it is well known that $\operatorname{VMO}^{**} = \operatorname{BMO}$ and there are many characterizations of the distance from a function$f$in $\operatorname{BMO}$ to $\operatorname{VMO}$ . When considering the Bloch space, results in the same vein are available with respect to the little Bloch space. In this paper such duality results and distance formulas are obtained by pure functional analysis. Applications include general Möbius invariant spaces such as$Q$_{$K$}-spaces, weighted spaces, Lipschitz–Hölder spaces and rectangular $\operatorname{BMO}$ of several variables.
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[9] Encomplexed Brown invariant of real algebraic surfaces in ℝ$P$^{3}
Johan Björklund Department of Mathematics, Uppsala University
mathscidoc:1701.01020
Arkiv for Matematik, 51, (2), 251-267, 2011.8
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We construct an invariant of parametrized generic real algebraic surfaces in ℝ$P$^{3}which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using self-intersections, which are real algebraic curves with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. In Kirby and Melvin (Local surgery formulas for quantum invariants and the Arf invariant, in$Proceedings of the Casson Fest$, Geom. Topol. Monogr.$7$, pp. 213–233, Geom. Topol. Publ., Coventry, 2004) the Brown invariant was expressed through a self-linking number of the self-intersection. We extend the definition of this self-linking number to the case of parametrized generic real algebraic surfaces.
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[10] Asymptotics for the size of the largest component scaled to “log$n$” in inhomogeneous random graphs
Tatyana S. Turova Centre for Mathematical Sciences, Lund University
Information Theory Optimization and Control Probability mathscidoc:1701.19001
Arkiv for Matematik, 51, (2), 371-403, 2012.1
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We study inhomogeneous random graphs in the subcritical case. Among other results, we derive an exact formula for the size of the largest connected component scaled by log$n$, with$n$being the size of the graph. This generalizes a result for the “rank-1 case”. We also investigate branching processes associated with these graphs. In particular, we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, also plays a crucial role in the subcritical case. However, now it is the$negative$solutions that come into play. We disclose their relationship to the distribution of the progeny of the branching process.
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