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作者：Biskup, Marek; Louidor, Oren
作者单位：University of California System; University of California Los Angeles; Technion Israel Institute of Technology
摘要：We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root, we prove that, in the limit as the depth of the tree tends to infinity, the suitably scaled and centered maximal time spent at any leaf converges to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale like object associated with square-root local-ti...
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作者：Muirhead, Stephen
作者单位：University of Melbourne
摘要：We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, on Z(d) or R-d, d >= 2, with correlations decaying at least algebraically with exponent alpha > 0, including the discrete Gaussian free field (d >= 3, alpha = d - 2), the discrete Gaussian membrane model (d >= 5, alpha = d - 4), and many other examples both discrete and continuous. In particular, we do not assume positive correlations. This result is new for all strongly correlated models (i.e.,...
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作者：Xu, Changji; Yang, Fan; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; Tsinghua University; Harvard University; University of California System; University of California Los Angeles
摘要：We consider Hermitian random band matrices H = (h(xy)) on the d-dimensional lattice (Z/LZ)(d), where the entries h(xy) = (h) over bar (yx) are independent centered complex Gaussian random variables with variances s(xy) = E|h(xy)|(2). The variance matrix S = (s(xy)) has a banded profile so that sxy is negligible if |x - y| exceeds the band width W. For dimensions d >= 7, we prove the bulk eigenvalue universality of H under the condition W >> L95/(d+95). Assuming that W >= L-epsilon for a small ...
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作者：Hen, Yu-Ting
作者单位：University of Victoria
摘要：In order to give a dual, annealed description of the two-dimensional stochastic heat equation (SHE) from regularizing the noise, we consider the Schrodinger semigroup of the many -body delta -Bose gas from mollifying the delta potentials. The main theorem proves the convergences of the corresponding approximate semigroups when they act on bounded functions. For the proof we introduce a mean -field Poisson system to expand the Feynman- Kac formula of the approximate semigroups. This expansion y...
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作者：Gess, Benjamin; Tsatsoulis, Pavlos
作者单位：University of Bielefeld
摘要：Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.
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作者：Dominguez, Tomas; Mourrat, Jean-christophe
作者单位：University of Toronto; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse regime, where the total number of nodes diverges while the average degree of a given node remains bounded. Our main contributions are a conjecture for the limit of this quantity, which we express in terms of a Hamilton-Jacobi equation posed over a space of probabi...
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作者：Burdzy, Krzysztof; Englander, Janos
作者单位：University of Washington; University of Washington Seattle; University of Colorado System; University of Colorado Boulder
摘要：We show that the spine of the Fleming-Viot process driven by Brownian motion in a bounded Lipschitz domain with Lipschitz constant less than 1 converges to Brownian motion conditioned to stay in the domain forever.
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作者：Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We prove that the absolute spectral gap of any monotone Markov chain coincides with its optimal Ollivier-Ricci curvature, where the word optimal refers to the choice of the underlying metric. Moreover, we provide a new expression in terms of local variations of increasing functions, which has several practical advantages over the traditional variational formulation using the Dirichlet form. As an illustration, we explicitly determine the optimal curvature and spectral gap of the nonconservativ...
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作者：Bodineau, Thierry; Gallagher, Isabelle; Saint-raymond, Laure; Simonella, Sergio
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Sapienza University Rome
摘要：We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.
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作者：Asselah, Amine; Forien, Nicolas; Gaudilliere, Alexandre
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sapienza University Rome; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Activated Random Walks, , on Zd d for any d >= 1, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during an exponential time of parameter lambda , after which it stays still in the frozen state, until another active particle shares its location, and turns it instantaneously back into activity. This model is known to have a phase transition, and we show that the critical densi...
