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作者：Benoist, Stephane; Hongler, Clement
作者单位：Columbia University; Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converges to nested CLE3. Our proof relies on the study of the coupling between the Ising model and its random cluster (FK) representation, and of the interactions between FK and Ising interfaces. The main idea is to construct an exploration process starting from the boundary of the domain, to discover the Ising loops and to...
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作者：Eberle, Andreas; Guillin, Arnaud; Zimmer, Raphael
作者单位：University of Bonn; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We introduce a new probabilistic approach to quantify convergence to equilibrium for (kinetic) Langevin processes. In contrast to previous analytic approaches that focus on the associated kinetic Fokker-Planck equation, our approach is based on a specific combination of reflection and synchronous coupling of two solutions of the Langevin equation. It yields contractions in a particular Wasserstein distance, and it provides rather precise bounds for convergence to equilibrium at the borderline ...
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作者：Ding, Jian; Xu, Changji
作者单位：University of Pennsylvania; University of Chicago
摘要：Place an obstacle with probability 1 - p independently at each vertex of Z(d), and run a simple random walk until hitting one of the obstacles. For d >= 2 and p strictly above the critical threshold for site percolation, we condition on the environment where the origin is contained in an infinite connected component free of obstacles, and we show that the following path localization holds for environments with probability tending to 1 as n -> infinity: conditioned on survival up to time n we h...
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作者：Kramkov, Dmitry; Pulido, Sergio
作者单位：Carnegie Mellon University; Universite Paris Saclay; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)
摘要：Let psi be a multidimensional random variable. We show that the set of probability measures Q such that the Q-martingale S-t(Q) = E-Q[psi vertical bar F-t] has the Martingale Representation Property (MRP) is either empty or dense in L-infinity-norm. The proof is based on a related result involving analytic fields of terminal conditions (psi (x))(x)(is an element of U) and probability measures (Q(x))(x)(is an element of U) over an open set U. Namely, we show that the set of points x is an eleme...
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作者：Kim, Ildoo; Kim, Kyeong-Hun; Lim, Sungbin
作者单位：Korea University
摘要：In this article, we present an L-p-theory (p >= 2) for the semi-linear stochastic partial differential equations (SPDEs) of type partial derivative(alpha)(t)u = L(omega,t,x)u + f(u) + partial derivative(beta)(t) Sigma(infinity)(k=1)integral(t)(0)(Lambda(k)(omega,t,x)u + g(k)(u)) dw(t)(k), where alpha is an element of (0,2), beta < alpha + 1/2 and partial derivative(alpha)(t) and partial derivative(beta)(t) denote the Caputo derivatives of order alpha and beta, respectively. The processes omega...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general method for lower bounds on fluctuations. The method is used to obtain new results for the stochastic traveling salesman problem, the stochastic minimal matching problem, the random assignment problem, the Sherrington-Kirkpatrick model of spin glasses, first-pa...
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作者：Gwynne, Ewain; Miller, Jason
作者单位：Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：In a recent series of works, Miller and Sheffield constructed a metric on root 8/3-Liouville quantum gravity (LQG) under which root 8/3-LQG surfaces (e.g., the LQG sphere, wedge, cone and disk) are isometric to their Brownian surface counterparts (e.g., the Brownian map, half-plane, plane and disk). We identify the metric gluings of certain collections of independent root 8/3-LQG surfaces with boundaries identified together according to LQG length along their boundaries. Our results imply in p...
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作者：Chong, Carsten; Kevei, Peter
作者单位：Technical University of Munich; Technical University of Munich; Szeged University
摘要：We investigate the moment asymptotics of the solution to the stochastic heat equation driven by a (d + 1)-dimensional Levy space-time white noise. Unlike the case of Gaussian noise, the solution typically has no finite moments of order 1 + 2/d or higher. Intermittency of order p, that is, the exponential growth of the pth moment as time tends to infinity, is established in dimension d = 1 for all values p is an element of (1, 3), and in higher dimensions for some p is an element of (1, 1 2/d)....
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作者：Balazs, Marton; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Bristol; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution, the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob tr...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider Z(d), d >= 3. We investigate the vacant set V-u of random interlacements in the strongly percolative regime, the vacant set V of the simple random walk and the excursion set E->=alpha of the Gaussian free field in the strongly percolative regime. We consider the large deviation probability that the adequately thickened component of the boundary of a large box centered at the origin in the respective vacant sets or excursion set leaves in the box a macroscopic volume in its compleme...
