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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：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：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 ...
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作者：Kim, Seonwoo
作者单位：Seoul National University (SNU)
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作者：Roeckner, Michael; Su, Yiming; Zhang, Deng
作者单位：University of Bielefeld; Zhejiang University of Technology; Shanghai Jiao Tong University
摘要：In this paper, we present a pathwise construction of multi-soliton solutions for focusing stochastic nonlinear Schrodinger equations with linear multiplicative noise, in both the L-2-critical and subcritical cases. The constructed multi-solitons behave asymptotically as a sum of K solitary waves, where K is any given finite number. Moreover, the con-vergence rate of the remainders can be of either exponential or polynomial type, which reflects the effects of the noise in the system on the asym...
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作者：Chen, Xinxin; Garban, Christophe; Shekhar, Atul
作者单位：Beijing Normal University; 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; CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France
摘要：In this work, we characterize all the point processes 0 = ?iEN 8xi on R which N/ are left invariant under branching Brownian motions with critical drift - 2. Our characterization holds under the only assumption that 0 is locally finite and 0CR+) < oo almost surely.
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作者：Hall, Brian C.; Ho, Ching-Wei
作者单位：University of Notre Dame; Academia Sinica - Taiwan
摘要：We consider a family of free multiplicative Brownian motions b(s,tau) parametrized by a real variance parameter s and a complex covariance parameter tau. We compute the Brown measure mu(s,r) of ub(s,tau) where u is a unitary element freely independent of b(s,tau). We find that mu(s,r) has a simple structure, with a density in logarithmic coordinates that is constant in the tau-direction. These results generalize those of Driver-Hall-Kemp and Ho-Thong for the case tau = s. We also establish a r...
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作者：Basak, Anirban
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru
摘要：We consider an Erdos-Renyi graph G(n, p) on n vertices with edge probability p such that log n log log n np n1/2-o(1), () and derive the upper tail large deviations of.(G(n, p)), the largest eigenvalue of its adjacency matrix. Within this regime we show that, for p n -2/3 the log-probability of the upper tail event of.(G(n, p)) equals to that of planting a clique of an appropriate size (upon ignoring smaller order terms), while for p n -2/3 the same is given by that of the existence of a high ...
