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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...
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作者：Bauerschmidt, Roland; Park, Jiwoon; Rodriguez, Pierre -Francois
作者单位：University of Cambridge; Imperial College London
摘要：The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer -valued. In two dimensions and at sufficiently high temperature, we show that its macroscopic scaling limit on the torus is a multiple of the Gaussian free field. Our proof starts from a single renormalisation group step after which the integer -valued field becomes a smooth field, which we then analyse using the renormalisation group method. This paper also provides the foundation for the construction of ...
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作者：Busani, Ofer; Seppalainen, Timo; Sorensen, Evan
作者单位：University of Bonn; University of Wisconsin System; University of Wisconsin Madison
摘要：The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of the Busemann process of exponential last-passage percolation. It was independently discovered as the Busemann process of Brownian last-passage percolation by the second and third authors. We show that SH is the unique invariant distribution and an attractor of the KPZ fixed point under conditions on th...
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作者：Tourniaire, Julie
作者单位：University of Vienna
摘要：We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift - mu and killed upon reaching 0, starting with N particles. More precisely, particles branch at rate rho /2 in the interval [ 0, 1], for some rho > 1, and at rate 1/2 in (1, +infinity ). The drift mu(rho) is chosen in such a way that, heuristically, the system is critical in some sense: the number of particles stays roughly constant before it event...
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作者：Dembo, Amir; Okada, Izumi
作者单位：Stanford University; Chiba University
摘要：We establish both the lim sup and the lim inf law of the iterated logarithm (LIL) for the capacity of the range of a simple random walk in any dimension d >= 3. While for d >= 4, the order of growth in n of such LIL at dimension d matches that for the volume of the random walk range in dimension d - 2, somewhat surprisingly this correspondence breaks down for the capacity of the range at d = 3. We further establish such LIL for the Brownian capacity of a three-dimensional Brownian sample path ...
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作者：Iksanov, Alexander; Kolesko, Konrad; Meiners, Matthias
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw; Justus Liebig University Giessen
摘要：Consider a supercritical Crump-Mode-Jagers process (Z(t)(phi))(t >= 0) counted with a random characteristic phi. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that, under some mild assumptions, e(-alpha t)Z(t )(phi)converges almost surely as t ->infinity to aW. Here, alpha>0 is the Malthusian parameter, a is a constant and W is the limit of Nerman's martingale, which is positive on the survival event. In this general situation, under additional ...
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作者：Rudelson, Mark
作者单位：University of Michigan System; University of Michigan
摘要：Let A be an nxn x n random matrix with independent identically distributed nonconstant sub-Gaussian entries. Then for any k <= c ,J n , rank (A) >= n - k with probability at least 1 - exp ( - c l kn) .
