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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：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：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：Adamczak, Radoslaw; Pivovarov, Peter; Simanjuntak, Paul
作者单位：University of Warsaw; University of Missouri System; University of Missouri Columbia
摘要：We establish central limit theorems for the volumes of intersections of Bpn (the unit ball of in p) with uniform random subspaces of codimension d for fixed d and n -> infinity. As a corollary we obtain higher-order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan-Klartag version of CLT for convex bodies. We also obtain a central limit theorem for the Minkowski functional of the intersection body of Bnp, evalua...
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作者：Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
作者单位：Technion Israel Institute of Technology; Beijing Institute of Technology
摘要：Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model the total occupation measure is known to have a continuously differentiable density (l(x))(x is an element of R), and we write (l(x))(x is an element of R )for its derivative. Although the process (l(x))(x >= 0) is not Markov, we prove that the pair(l(x), l(x))(x >= 0 )is a time-homogeneous Markov proc...
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作者：Casanova, Adrian Gonzalez; Tobias, Andras; Valesin, Daniel
作者单位：Universidad Nacional Autonoma de Mexico; Budapest University of Technology & Economics; University of Warwick
摘要：We introduce and study an interacting particle system evolving on the ddimensional torus (Z/NZ)d. Each vertex of the torus can be either empty or occupied by an individual of type lambda is an element of (0, infinity). An individual of type lambda dies with rate one and gives birth at each neighboring empty position with rate lambda; moreover, when the birth takes place, the newborn individual is likely to have the same type as the parent but has a small probability of being a mutant. A mutant...
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作者：Fehrman, Benjamin
作者单位：University of Oxford
摘要：We prove that diffusion equations with a space-time stationary and ergodic, divergence -free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skewsymmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time -dependent, spatially -homogenous transport which, for mildly decorrelating fields, converges...
