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作者：Dauvergne, Duncan; Sly, Allan
作者单位：University of Toronto; Princeton University
摘要：We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected region when infected and susceptible particles move at the same speed. In this paper we establish a linear growth rate when infected and susceptible particles move at different speeds, answering an open problem from their work. Our proof combines an intricate coupling of Poisson processes with a stre...
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作者：Durhuus, Bergfinnur; Unel, Meltem
作者单位：University of Copenhagen
摘要：We consider planar rooted random trees whose distribution is even for fixed height h and size N and whose height dependence is of exponential form e(-mu h). Defining the total weight for such trees of fixed size to be Z((mu)) (N) , we determine its asymptotic behaviour for large N, for arbitrary real values of mu. Based on this we identify the local limit of the corresponding probability measures and find a transition at mu = 0 from a single spine phase to a multi-spine phase. Correspondingly,...
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作者：Guillin, Arnaud; Nectoux, Boris; Wu, Liming
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS)
摘要：In this work, we prove the existence and the uniqueness of a quasi-stationary distribution for hypoelliptic Hamiltonian dynamics for a system of N particles in R-d interacting with Lennard-Jones type potentials or with repulsive Coulomb potentials.
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作者：Dario, Paul; Harel, Matan; Peled, Ron
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Northeastern University; Tel Aviv University
摘要：We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, in the following cases. It is shown that for real-valued random-field random surfaces of the & nabla; phi type with a uniformly convex interaction potential: (i) The gradient of the surface delocalizes in dimensions 1 <= d <= 2 and localizes...
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作者：Borodin, Alexei; Duits, Maurice
作者单位：Massachusetts Institute of Technology (MIT); Royal Institute of Technology
摘要：We study random domino tilings of the Aztec diamond with a biased 2 x 2 periodic weight function and associate a linear flow on an elliptic curve to this model. Our main result is a double integral formula for the correlation kernel, in which the integrand is expressed in terms of this flow. For special choices of parameters the flow is periodic, and this allows us to perform a saddle point analysis for the correlation kernel. In these cases we compute the local correlations in the smooth diso...
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作者：Neeman, Joe; Radin, Charles; Sadun, Lorenzo
作者单位：University of Texas System; University of Texas Austin
摘要：The analysis of large simple graphs with extreme values of the densities of edges and triangles has been extended to the statistical structure of typical graphs of fixed intermediate densities, by the use of large deviations of Erdos-Renyi graphs. We prove that the typical graph exhibits sharp singularities as the constraining densities vary between different curves of extreme values, and we determine the precise nature of the singularities. The extension to graphs with fixed densities of edge...
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作者：Bryc, Wlodek; Kuznetsov, Alexey; Wang, Yizao; Wesolowski, Jacek
作者单位：University System of Ohio; University of Cincinnati; York University - Canada; Warsaw University of Technology
摘要：We provide a probabilistic description of the stationary measures for the open KPZ on the spatial interval [0, 1] in terms of a Markov process Y, which is a Doob's h transform of the Brownian motion killed at an exponential rate. Our work builds on a recent formula of Corwin and Knizel which expresses the multipoint Laplace transform of the stationary solution of the open KPZ in terms of another Markov process T: the continuous dual Hahn process with Laplace variables taking on the role of tim...
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作者：Nestoridi, Evita; Sly, Allan
作者单位：Princeton University
摘要：We study a natural random walk on thenxn uni-upper triangular matrices, with entries in Z/mZ, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is O(m(2)n log n + n(2)m(o(1))). This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H + x A with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched ...
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作者：Gaudreau Lamarre, Pierre Yves; Lin, Yier; Tsai, Li-Cheng
作者单位：University of Chicago; Utah System of Higher Education; University of Utah
摘要：In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter root epsilon in front of the noise and let epsilon -> 0. We prove that the one-point large deviation rate function has a 3/2 power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the solution of the KPZ equation as epsilon -> 0. This confirms the physics prediction in Hartmann et al. (Phys Rev ...
