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作者：Djete, Mao Fabrice; Possamai, Dylan; Tan, Xiaolu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Federal Institutes of Technology Domain; ETH Zurich; Chinese University of Hong Kong
摘要：We study the McKean-Vlasov optimal control problem with common noise which allow the law of the control process to appear in the state dynamics under various formulations: strong and weak ones, Markovian or non-Markovian. By interpreting the controls as probability measures on an appropriate canonical space with two filtrations, we then develop the classical measurable selection, conditioning and concatenation arguments in this new context, and establish the dynamic programming principle under...
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作者：Berestycki, Julien; Brunet, Eric; Nolen, James; Penington, Sarah
作者单位：University of Oxford; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Duke University; University of Bath
摘要：The Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that, as N -> oo, the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is ...
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作者：Hermon, Jonathan; Li, Shuangping; Yao, Dong; Zhang, Lingfu
作者单位：University of British Columbia; Princeton University; Jiangsu Normal University; Princeton University
摘要：In this paper, we consider coalescing random walks on a general connected graph G = (V, E). We set up a unified framework to study the leading order of the decay rate of P-t , the expectation of the fraction of occupied sites at time t, particularly for the 'Big Bang' regime where t << t(coal) :=E(inf{s : There is only one particle at time s}). Our results show that P-t satisfies certain 'mean-field behaviors' if the graphs satisfy certain 'transience-like' conditions. We apply this framework ...
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作者：Bruno, Stefano; Gess, Benjamin; Weber, Hendrik
作者单位：University of Bath; University of Bielefeld
摘要：We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in space. The coefficients are assumed to be Holder continuous, and the cases of smooth coefficients of, at most, linear growth as well as root u are covered by our as-sumptions. The regularity obtained is consistent with the optimal regularity derived for the deterministic porous medium equat...
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作者：Goswami, Subhajit; Rodriguez, Pierre-Francois; Severo, Franco
作者单位：Tata Institute of Fundamental Research (TIFR); Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the Gaussian free field phi on Z(d), for d >= 3, and give sharp bounds on the probability that the radius of a finite cluster in the excursion set {phi >= h} exceeds a large value N for any height h not equal h(*), where h(*) refers to the corresponding percolation critical parameter. In dimension 3, we prove that this probability is subexponential in N and decays as exp{-pi/6 (h - h(*))(2) N/logN} as N -> infinity to principal exponential order. When d >= 4, we prove that these ta...
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作者：Sly, Allan; Zhang, Lingfu
作者单位：Princeton University
摘要：For the Voter Model on Z(d), d >= 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899-955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Z(d).
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作者：Berger, Noam; Cohen, Moran; Deuschel, Jean-Dominique; Guo, Xiaoqin
作者单位：Technical University of Munich; Hebrew University of Jerusalem; Technical University of Berlin; University System of Ohio; University of Cincinnati
摘要：We prove an elliptic Harnack inequality at large scale on the lattice Z(d) for nonnegative solutions of a difference equation with balanced i.i.d. coefficients which are not necessarily elliptic. We also identify the optimal constant in the Harnack inequality. Our proof relies on a quantitative homogenization result of the corresponding invariance principle to Brownian motion and on percolation estimates. As a corollary of our main theorem, we derive an almost optimal Holder estimate.
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作者：Dunlap, Alexander; Gu, Yu
作者单位：New York University; University System of Maryland; University of Maryland College Park
摘要：We consider a nonlinear stochastic heat equation in spatial dimension d = 2, forced by a white-in-time multiplicative Gaussian noise with spatial correlation lengths epsilon > 0 but divided by a factor of root log epsilon(-1). We impose a condition on the Lipschitz constant of the nonlinearity so that the problem is in the weak noise regime. We show that, as epsilon down arrow 0, the one-point distribution of the solution converges, with the limit characterized in terms of the solution to a fo...
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作者：Dauvergne, Duncan; Sarkar, Sourav; Virag, Balint
作者单位：University of Toronto; University of Cambridge
摘要：We show that geodesics in the directed landscape have 3/2-variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscape environment around an interior point have a small-scale limit. This limit is given in terms of the directed landscape with Brownian-Bessel boundary conditions. The environments around different interior points are asymptotically independent. We give tail bounds with optimal exponents for geodesic and weight function ...
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作者：Giacomin, Giambattista; Lacoin, Hubert
作者单位：Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We continue the study, initiated in (J. Eur. Math. Soc. (JEMS) 20 (2018) 199-257), of the localization transition of a lattice free field phi = (phi(x))(x is an element of Zd), d >= 3, in presence of a quenched disordered substrate. The presence of the substrate affects the interface at the spatial sites in which the interface height is close to zero. This corresponds to the Hamiltonian Sigma(x is an element of Zd) (beta omega(x) + h)delta(x), where delta(x) = 1([-1,1])(phi(x)), and (omega(x))...
