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作者：Bauerschmidt, Roland; Hofstetter, Michael
作者单位：University of Cambridge
摘要：For 0 < beta < 6 pi, we prove that the distribution of the centred maximum of the e-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as epsilon -> 0. Our proof relies on a strong coupling at all scales of the sine-Gordon field with the Gaussian free field, of independent interest, and extensions of existing methods for the maximum of the lattice Gaussian free field.
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作者：Geng, Xi; Ouyang, Cheng; Tindel, Samy
作者单位：University of Melbourne; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
摘要：This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H > 1/4 and understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.
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作者：Izyurov, Konstantin
作者单位：University of Helsinki
摘要：We prove the convergence of multiple interfaces in the critical planar q = 2 random cluster model and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple SLE16/3 coincides with the bulk spin correlation in the critical Ising model in the half-plane, after formally replacing a position of each spin and its complex conjugate with a pair of points on the real line. As a corollary we recover Belavin-Polyakov-Zamolodc...
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作者：Magazinov, Alexander; Peled, Ron
作者单位：Tel Aviv University
摘要：We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp-Lieb concentration inequality and an inequality quantifying log-concavity of marginals in a manner suitable for obtaining variance and tail probability bounds. These inequalities are applied to the statistical mechanics problem of estimating the fluctuations of random surfaces of the del phi type. The classical Brascamp-Lieb inequality bounds the fluctuation...
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作者：Aru, Juhan; Lupu, Titus; Sepulveda, Avelio
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universidad de Chile
摘要：Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining the law of the extremal distance between and the boundary of the unit disk. More surprisingly, we also compute the joint law of these conformal radius and extremal distance. This law involves first and last hitting times of a one-dimensional...
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作者：Paouris, Grigoris; Tikhomirov, Konstantin; Valettas, Petros
作者单位：Texas A&M University System; Texas A&M University College Station; University System of Georgia; Georgia Institute of Technology; University of Missouri System; University of Missouri Columbia; University of Missouri System; University of Missouri Columbia
摘要：We consider the problem of estimating small ball probabilities P[f (G) <= delta E f (G)} for subadditive, positively homogeneous functions f with respect to the Gaussian measure. We establish estimates that depend on global parameters of the underlying function, which take into account analytic and statistical measures, such as the variance and the L-1-norms of its partial derivatives. This leads to dimension-dependent bounds for small ball and lower small deviation estimates for seminorms whe...
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作者：Dello Schiavo, Lorenzo
作者单位：Institute of Science & Technology - Austria
摘要：We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d >= 2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet-Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 7...
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作者：Johansson, Kurt; Rahman, Mustazee
作者单位：Royal Institute of Technology; Durham University
摘要：This article studies the inhomogeneous geometric polynuclear growth model; the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the two-time distribution. Asymptotics of the two-time distribution in the KPZ-scaling limit is then considered, extending to two times several single-time distributions in the KPZ universality class.
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作者：Bowditch, Adam; Sun, Rongfeng
作者单位：National University of Singapore
摘要：In this paper, we construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Furthermore, we show that almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman.
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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...
