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作者：Kolb, Martin; Savov, Mladen
作者单位：University of Paderborn; Bulgarian Academy of Sciences
摘要：In this paper, we study the behavior of Brownian motion conditioned on the event that its local time at zero stays below a given increasing function f up to time T. For a class of nonincreasing functions f, we show that the conditioned process converges, as T -> infinity, to a limit process and we derive necessary and sufficient conditions for the limit to be transient. In the transient case, the limit process is described explicitly, and in the recurrent case we quantify the entropic repulsio...
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作者：Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We construct a conformal welding of two Lionville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE), thereby resolving a variant of a conjecture of Peter Jones. We also demonstrate some surprising symmetries of this construction, which are consistent with the belief that (path-decorated) random planar maps have (SLE-decorated) Liouville quantum gravity as a scaling limit. We present several precise conj...
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作者：Cerrai, Sandra; Salins, Michael
作者单位：University System of Maryland; University of Maryland College Park
摘要：In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski Kramers approximation is not only valid for small time, but in the zero noise limi...
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作者：Panagiotou, Konstantinos; Stufler, Benedikt; Weller, Kerstin
作者单位：University of Munich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the uniform random graph C-n with n vertices drawn from a subcritical class of connected graphs. Our main result is that the resealed graph C-n / root n converges to the Brownian continuum random tree T-e multiplied by a constant scaling factor that depends on the class under consideration. In addition, we provide sub-Gaussian tail bounds for the diameter D (C-n) and height H(C-n(center dot)) of the rooted random graph C-n(center dot) We give analytic expressions for the scaling facto...
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作者：Berard, Jean; Ramirez, Alejandro
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Pontificia Universidad Catolica de Chile
摘要：We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice Z with jump rates D-R for red particles and D-B for blue particles, the interaction rule being that blue particles turn red upon contact with a red particle. The initial condition consists of i.i.d. Poisson particle numbers at each site, with particles at the left of the origin being red, while part...
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作者：Lupu, Titus
作者单位：Universite Paris Saclay
摘要：It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops (loop soup) of parameter 1/2 associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter 1/2 do not percol...
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作者：Carmona, Philippe; Gia Bao Nguyen; Petrelis, Nicolas
作者单位：Nantes Universite; Universidad de Chile
摘要：In this paper, we investigate a model for a 1 1 dimensional self interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by beta and f, respectively. The IPDSAW is known to undergo a collapse transition at beta(c). We provide the precise asymptotic of the free energy close to criticality, that is, we show that f (beta(c) - epsilon) similar to gamma epsilon(3/2) where gamma is compu...
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作者：Paulin, Daniel; Mackey, Lester; Tropp, Joel A.
作者单位：National University of Singapore; Stanford University; California Institute of Technology
摘要：This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.
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作者：Fyodorov, Y. V.; Khoruzhenko, B. A.; Simm, N. J.
作者单位：University of London; Queen Mary University London
摘要：The goal of this paper is to establish a relation between characteristic polynomials of N x N GUE random matrices H as N ->infinity, and Gaussian processes with logarithmic correlations. We introduce a regularized version of fractional Brownian motion with zero Hurst index, which is a Gaussian process with stationary increments and logarithmic increment structure. Then we prove that this process appears as a limit of D-N(Z) = -log vertical bar det(H - zI) on mesoscopic scales as N -> infinity....
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作者：Abert, Miklos; Glasner, Yair; Virag, Balint
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Ben-Gurion University of the Negev; University of Toronto; University of Toronto
摘要：We give an explicit bound on the spectral radius in terms of the densities of short cycles in finite d-regular graphs. It follows that the a finite d-regular Ramanujan graph G contains a negligible number of cycles of size less than c log log vertical bar G vertical bar. We prove that infinite d-regular Ramanujan unimodular random graphs are trees. Through Benjamini-Schramm convergence this leads to the following rigidity result. If most eigenvalues of a d-regular finite graph G fall in the Al...
