We consider ASEP on a bounded interval and on a half‐line with sources and sinks. On the full line, Bertini and Giacomin in 1997 proved convergence under weakly asymmetric scaling of the height function to the solution of the KPZ equation. We prove here that under similar weakly asymmetric scaling of the sources and sinks as well, the bounded interval ASEP height function converges to the KPZ equation on the unit interval with Neumann boundary conditions on both sides (different parameter for each side), and likewise for the half‐line ASEP to KPZ on a half‐line. This result can be interpreted as showing that the KPZ equation arises at the triple critical point (maximal current / high density / low density) of the open ASEP.

New, “big data” sources allow measurement of city characteristics and outcomevariables at higher collection frequencies and more granular geographic scales thanever before. However, big data will not solve large urban social science questionson its own. Big urban data has the most value for the study of cities when it allowsmeasurement of the previously opaque, or when it can be coupled with exogenous shocksto people or place. We describe a number of new urban data sources and illustrate howthey can be used to improve the study and function of cities. We rst show how GoogleStreet View images can be used to predict income in New York City, suggesting thatsimilar imagery data can be used to map wealth and poverty in previously unmeasuredareas of the developing world. We then discuss how survey techniques can be improved tobetter measure willingness to pay for urban amenities. Finally, we explain how Internetdata is being used to improve the quality of city services.

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In this paper, we prove a necessary and sufficient condition for Tracy-Widom law of Wigner matrices. Consider N×N symmetric Wigner matrices H with Hij=N−1/2xij, whose upper right entries xij (1≤i<j≤N) are i.i.d. random variables with distribution μ and diagonal entries xii (1≤i≤N) are i.i.d. random variables with distribution $\wt \mu$. The means of μ and $\wt \mu$ are zero, the variance of μ is 1, and the variance of $\wt \mu$ is finite. We prove that Tracy-Widom law holds if and only if $\lim_{s\to \infty}s^4\p(|x_{12}| \ge s)=0$. The same criterion holds for Hermitian Wigner matrices.

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