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作者：Bartholdi, Laurent; Erschler, Anna
作者单位：Universite PSL; Ecole Normale Superieure (ENS); University of Gottingen
摘要：We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment with non-trivial boundary, and show that this criterion is useful to establish exponential word growth of groups. We construct groups of exponential growth such that all finitely supported (not necessarily symmetric, possibly degenerate) random walks on these groups have trivial boundary. This gives a negative...
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作者：Armendariz, Ines; Grosskinsky, Stefan; Loulakis, Michail
作者单位：University of Buenos Aires; University of Warwick; National Technical University of Athens
摘要：Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process o...
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作者：Knowles, Antti; Yin, Jun
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Wisconsin System; University of Wisconsin Madison
摘要：We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random matrices. In particular, it may be used to obtain local laws for matrix ensembles that are anisotropic in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity. For definiteness, we present the method for sample covariance matrices of the f...
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作者：Chen, Wei-Kuo; Dey, Partha; Panchenko, Dmitry
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign; University of Toronto
摘要：We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar, inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd p-spin interactions for , we prove the central limit theorem for the free energy at any temperature and give an explicit formula for ...
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作者：Duhalde, Xan; Duquesne, Thomas
作者单位：Sorbonne Universite
摘要：We consider super processes whose spatial motion is the d-dimensional Brownian motion and whose branching mechanism is critical or subcritical; such processes are called -super Brownian motions. If , where is the lower index of at , then the total range of the -super Brownian motion has an exact packing measure whose gauge function is , where . More precisely, we show that the occupation measure of the -super Brownian motion is the g-packing measure restricted to its total range, up to a deter...
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作者：Dommers, Sander
作者单位：University of Bologna
摘要：We study the metastability of the ferromagnetic Ising model on a random r-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like when the inverse temperature and the number of vertices n is large enough but fixed. The proof is based on the so-called pathwise approach and bounds on the isoperimetric number of random regular graphs.
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作者：Silvestri, Vittoria
作者单位：University of Cambridge
摘要：We study the fluctuations of the outer domain of Hastings-Levitov clusters in the small particle limit. These are shown to be given by a continuous Gaussian process taking values in the space of holomorphic functions on , of which we provide an explicit construction. The boundary values of are shown to perform an Ornstein-Uhlenbeck process on the space of distributions on the unit circle , which can be described as the solution to the stochastic fractional heat equation Equation ID=Equ34 Media...
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作者：Roch, Sebastien; Sly, Allan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Princeton University
摘要：Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which ...
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作者：Kortchemski, Igor
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym,-Galton-Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.
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作者：Lewicka, Marta; Manfredi, Juan J.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We present a probabilistic approach to the obstacle problem for the p-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.
