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# The distribution of landed property

**Article**

*in*Physica A: Statistical Mechanics and its Applications 388(21):4619-4623 · February 2009

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DOI: 10.1016/j.physa.2009.07.019 · Source: arXiv

Cite this publicationAbstract

The distribution of property is established through various mechanisms. In
this paper we study the acreage distribution of land plots owned by natural
persons in the Zl\'{\i}n Region of the Czech Republic. We show that the data
are explained in terms of a simple model in which the inheritance and market
behavior are combined.

- ... Modern real estate developments are typically marketed with well-chosen property names [17] which can be interpreted as a form of place branding [18], rather than just a lot or street number. This is a phenomenon that has attracted research on the basis of memetics [19], a branch of studies on information that laid the foundation of the empirical research by Exner et al. [20] on land ownership that appeared in the planning literature in Vasishth [21], Mehmood [22], and Lai et al. [23]. So far, no attempt has been made to interpret built heritage as objective signs, though Robertson [24] had related memes and Poddubnykh [25] memory to heritage conservation interpretation. ...ArticleFull-text available
- Feb 2019

A global real estate revolution has been transforming the urban landscape everywhere. Development and redevelopment projects have mixed with, if not become an integral part of, real estate construction. At the same time, there is a drive to commodification in this revolution, as shown by a growing trend to conserve built heritage in new development projects characterised by the rise of museums. This paper reviews some examples of attempts in various parts of the world to combine real estate development and conservation and applies the fourth Coase theorem to explore how built heritage conservation and urban renewal in Hong Kong, hitherto problematic in terms of their invasion of private property, can become a win-win outcome in the context of this global real estate revolution.

- CITIES grow in a way that might be expected to resemble the growth of two-dimensional aggregates of particles, and this has led to recent attempts1á¤-3 to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion-limited aggregation4,5 (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies1. The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming á¤~development unitsá¤™ (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the clusterá¤™s branches. Here we show that an alternative model, in which development units are correlated rather than being added to the cluster at random, is better able to reproduce the observed morphology of cities and the area distribution of sub-clusters (á¤~towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model6á¤-8 in the presence of a density gradient9, is motivated by the fact that in urban areas development attracts further development. The model offers the possibility of predicting the global properties (such as scaling behaviour) of urban morphologies.
- Jan 2007
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- M Patriarca
- A Chakraborti
- E Heinsalu
- G Germano

Patriarca M, Chakraborti A, Heinsalu E and Germano G 2007 Eur. Phys. J. B 57 219-224- Jan 2008
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- M Knape
- R Neininger

Knape M and Neininger R 2008 Methodol. Comput. Appl. Probability 10 507-529- Jan 2002
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- Z F Huang
- S Solomon

Huang Z F and Solomon S 2002 Physica A 306 412-422- Jan 1998
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- R V Sole

Sole R V and Alonso D 1998 Adv. Complex Systems 1 203-220- Jan 2006
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- C Leung
- N Chen

Leung C K Y and Chen N K 2006 J. Real Estate Research 28 293-320- Jan 2005
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- T Kaizoji

Kaizoji T 2005 Physica A 347 575-582- Jan 1978

- O Urban

Urban O 1978 Capitalism and Czech Society (in Czech; Prague: Svoboda)- Jan 1999
- 1987-1990

- B Derrida
- S C Manrubia
- D Zanette

Derrida B, Manrubia S C and Zanette D H 1999 Phys. Rev. Lett. 82 1987-1990- Jan 2002
- 441-468

- L Devroye
- R Neininger

Devroye L and Neininger R 2002 Adv. Appl. Probability 34 441-468- Jan 2002
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- D Sornette

Sornette D 2002 Physica A 309 403-418- Jan 2008
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- P Exner

Exner P. andŠebaandˇandŠeba P 2008 J. Phys. A: Math. Gen. 41 045004- Jan 2006
- 89-95

- S Laemmer
- B Gehlsen
- D Helbing

Laemmer S, Gehlsen B and Helbing D 2006 Physica A 363 89-95- Jan 1999

- S Blackmore

Blackmore S 1999 The Meme Machine (Oxford: Oxford University Press)- Jan 2002
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- S C Manrubia
- D Zanette

Manrubia S C and Zanette D H 2002 J. Theor. Biology 216 461-477- Jan 2000
- 383-400

- R White
- G Engelen

White R and Engelen G 2000 Computers, Environment and Urban Systems 24 383-400- Article
- Dec 2004
- PHYSICA A

In this study, we investigate quantitatively statistical properties of a ensemble of land prices in Japan in the period from 1981 to 2002, corresponding to a period of bubbles and crashes. We found that the tail of the complementary cumulative distribution function of the ensemble of land prices in the high price range is well described by a power-law distribution, P(S > x) similar to x(-alpha), and furthermore that as the power-law exponents alpha approached unity, bubbles collapsed. (C) 2004 Published by Elsevier B.V. - Jan 2001
- 29-38

- M Baron
- A Rukhin

Baron M and Rukhin A L 2001 Stat. and Probab. Lett. 55 29-38- We review some statistical many-agent models of economic and social systems inspired by microscopic molecular models and discuss their stochastic interpretation. We apply these models to wealth exchange in economics and study how the relaxation process depends on the parameters of the system, in particular on the saving propensities that define and diversify the agent profiles.
- We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well.
- Article
- Mar 2005
- PHYSICA A

The aim of this paper is to investigate the statistical properties of the spatial distribution for each of the towns in Japan, of the number of large income earners living in them and their total income. Using a Japanese database of high-income taxpayers for two consecutive years, 1997 and 1998, we found that the complementary cumulative distribution functions of the number of large income earners and the total income of all of them for each of the towns is well described by a power-law distribution with an exponent close to 2. Our results show that large income earners tend to gravitate to a small number of towns, leading to the evolution of so-called high-class residential streets and neighborhoods. - Article
- Oct 2000
- PHYSICA A

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns. - Article
- Jan 2005
- PHYSICA A

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies. - Article
- Sep 2000
- COMPUT ENVIRON URBAN

An emerging branch of geocomputing involves the modelling of spatial processes. A variety of techniques are being used, the most important being traditional regionalized system dynamics approaches, multi-agent systems, and cellular automata (CA). The techniques are frequently combined to model processes operating at different spatial scales. Urban and regional models based on CA give good representations of the spatial dynamics of land use. In a current application, a cellular model of The Netherlands at 500 m resolution is driven by a macro-scale dynamical spatial interaction model defined on 40 economic regions; this model is in turn driven by national planning projections and policy goals. Given the national totals, the macro-scale model generates regional demands for population and a number of economic activities. These demands are translated into demands for cell space, which the CA then attempts to locate. In turn, information on conditions at the cellular level, such as the quantity and quality of land available to various activities and actual densities at the cellular scale, are returned to the regional model to modify parameter values there. Linking the two models operating at the two scales improves the performance of both. The results of high-resolution modelling of spatial dynamics raise several methodological issues. One of the most pressing concerns evaluation of the results. Another issue concerns predictability. To the extent that these models capture the evolving nature of real cities and regions, they cannot be strictly predictive. - Article
- Apr 2002
- PHYSICA A

We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Lévy-like distribution, and the cross-correlation between relative updated wealths is the origin of the nontrivial properties of returns, including the power-law distribution with exponent outside the stable Lévy regime and the long-range persistence of volatility correlations. - Article
- Jan 2007

The size distribution of land plots is a result of land allocation processes in the past. In the absence of regulation this is a Markov process leading an equilibrium described by a probabilistic equation used commonly in the insurance and financial mathematics. We support this claim by analyzing the distribution of two plot types, garden and build-up areas, in the Czech Land Registry pointing out the coincidence with the distribution of prime number factors described by Dickman function in the first case. - Article
- Jun 2002
- ADV APPL PROBAB

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method. - Rainforests are legendary because of their extreme species richness. In the richest rain forests every second tree on a hectare is a different species. As a consequence, most species are rare. Using field data from studies in different parts of the world, we show that species-rich plots often display a distribution of number of species N_s(I) represented by I individuals with a power-law shape with Power laws are characteristic (but not exclusive) of systems poised close to critical points and this is supported by the analysis of the gap distribution over space in the Barro Colorado Island forest, which has been shown to be fractal. Here we propose a new model of rainforest dynamics which is able to account for a wide set of observations, strongly suggesting that indeed rainforests would be organized close to instability points, showing strongly path-dependent dynamics. To appear in: J. Complex Systems.
- Article
- Nov 2001
- STAT PROBABIL LETT

The distribution of stochastically discounted sums (perpetuities) is studied. For Bernoulli-type variables a canonical representation of this distribution is obtained, and it is proven to be singular continuous. In the asymptotic setting of the change-point estimation problem the limiting behavior of the posterior distribution is shown to be given by two independent perpetuities. - Article
- Jul 2002
- J THEOR BIOL

Surnames and non-recombining alleles are inherited from a single parent in a highly similar way. A simple birth-death model with mutations can accurately describe this process. Exponentially growing and constant populations are investigated, and we study how different compositions of the founder populations can be observed in present-day diversity distributions. We analyse different quantities in the statistically stationary state, both through analytic and numerical methods. Our results compare favourably to field data for family sizes in several countries. We discuss the relationship between the distribution of surnames and the genetic diversity of a population. - The cyclicality and volatility of property prices have been extensively documented. Many explanations have been proposed. This paper builds a simple dynamic general equilibrium model in which these often cited channels are assumed away. Instead, the role of intertemporal elasticity of substitution is highlighted. In this model, the land price can exhibit price cycles. Moreover, the land price always fluctuates more than the aggregate output. The welfare of different cohorts depends crucially on the land price at the period they were born. The implications of these results are discussed.
- Article
- Jan 2007
- REP PROG PHYS

This review deals with several microscopic (``agent-based'') models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation approaches in financial economics, we first give a summary of the Donangelo-Sneppen model of monetary exchange and compare it with related models in economics literature. Our selective review then outlines the main ingredients of some influential early models of multi-agent dynamics in financial markets (Kim-Markowitz, Levy-Levy-Solomon). As will be seen, these contributions draw their inspiration from the complex appearance of investors' interactions in real-life markets. Their main aim is to reproduce (and, thereby, provide possible explanations) for the spectacular bubbles and crashes seen in certain historical episodes, but they lack (like almost all the work before 1998 or so) a perspective in terms of the universal statistical features of financial time series. Comment: Long review. Accepted by Reports on Progress in Physics - We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution, we measure the distribution of ancestors appearing more than once in a given tree. After a transient time, the probability of repetition follows, up to a rescaling, a stationary distribution which we calculate both numerically and analytically. This distribution exhibits a universal shape with a non-trivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy illustrate the problem, which is relevant to the study of the real degree of diversity in closed interbreeding communities. Comment: Accepted for publication in Phys. Rev. Lett
- We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient. Comment: 10 pages, 10 figures, http://polymer.bu.edu/~hmakse/Home.html