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作者：Belius, David; Wu, Wei
作者单位：University of Basel; New York University; NYU Shanghai
摘要：We study a two-dimensional massless field in a box with potential V(del phi(.)) and zero boundary condition, where V is any symmetric and uniformly convex function. Naddaf-Spencer (Comm. Math. Phys. 183 (1997) 55-84) and Miller (Comm. Math. Phys. 308 (2011) 591-639) proved that the rescaled macroscopic averages of this field converge to a continuum Gaussian free field. In this paper, we prove that the distribution of local marginal cb(x), for any x in the bulk, has a Gaussian tail. We further ...
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作者：Kulik, Alexei; Scheutzow, Michael
作者单位：Wroclaw University of Science & Technology; Technical University of Berlin
摘要：We develop a new generalized coupling approach to the study of stochastic delay equations with Holder continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak solutions, and establish weak ergodic rates for the corresponding segment processes. We also prove, under additional smoothness assumptions on the coefficients, stabilization rates for the sensitivities in the initial value of the corresponding semigroups.
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作者：Beliaev, Dmitry; Muirhead, Stephen; Rivera, Alejandro
作者单位：University of Oxford; University of London; Queen Mary University London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii) events measurable with respect to the number of connected components of level or excursion sets of a given diffeomorphism class and (iii) persistence events. As an application of the covariance formula, we derive strong mixing bounds for to...
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作者：Landon, Benjamin; Lopatto, Patrick; Marcinek, Jake
作者单位：Massachusetts Institute of Technology (MIT); Harvard University
摘要：We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalized Wigner ensembles, provided that the first four moments of their matrix entries match. As an application, we extend results of Ben Arous-Bourgade and Feng-Wei that identify the limit of the maximal eigenvalue gap in the bulk of the GUE to all complex Hermitian generalized Wigner matrices.
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作者：Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a central limit theorem for the capacity of the range of a symmetric random walk on Z(5) , under only a moment condition on the step distribution. The result is analogous to the central limit theorem for the size of the range in dimension three, obtained by Jain and Pruitt in 1971. In particular, an atypical logarithmic correction appears in the scaling of the variance. The proof is based on new asymptotic estimates, which hold in any dimension d >= 5, for the probability that the ran...
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作者：Hermon, Jonathan; Sousi, Perla
作者单位：University of British Columbia; University of Cambridge
摘要：We consider the model of random walk on dynamical percolation introduced by Peres, Stauffer and Steif in (Probab. Theory Related Fields 162 (2015) 487-530). We obtain comparison results for this model for hitting and mixing times and for the spectral gap and log-Sobolev constant with the corresponding quantities for simple random walk on the underlying graph G, for general graphs. When G is the torus Z(n)(d) , we recover the results of Peres et al., and we also extend them to the critical case...
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作者：Hermon, Jonathan; Pymar, Richard
作者单位：University of British Columbia; University of London; Birkbeck University London
摘要：Oliveira conjectured that the order of the mixing time of the exclusion process with k-particles on an arbitrary n-vertex graph is at most that of the mixing-time of k independent particles. We verify this up to a constant factor for d-regular graphs when each edge rings at rate 1/d in various cases: (1) when d = Omega (log(n/k)n), (2) when gap := the spectral-gap of a single walk is O (1/log(4) n) and k >= n(Omega(1)), (3) when k asymptotic to n(a) for some constant 0 < a < 1. In these cases,...
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作者：Carlen, Eric; Carvalho, Maria; Loss, Michael
作者单位：Rutgers University System; Rutgers University New Brunswick; Universidade de Lisboa; University System of Georgia; Georgia Institute of Technology
摘要：We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, that is effective in the case of degenerate jump rates, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.
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作者：Saksman, Eero; Webb, Christian
作者单位：University of Helsinki; Aalto University
摘要：We prove that if omega is uniformly distributed on [0, 1], then as T -> infinity, t bar right arrow zeta (i omega T + it + 1/2) converges to a nontrivial random generalized function, which in turn is identified as a product of a very well-behaved random smooth function and a random generalized function known as a complex Gaussian multiplicative chaos distribution. This demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos-the latter...
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作者：Kajino, Naotaka; Murugan, Mathav
作者单位：Kobe University; University of British Columbia
摘要：We show that, for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimension strictly larger than two (sub-Gaussian estimates) imply the singularity of the energy measures with respect to the symmetric measure, verifying a conjecture by M. T. Barlow in (Contemp. Math. 338 (2003) 11-40). We also prove that in the contrary case of walk dimension two, that is, where full off-diagonal Gaussi...
