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作者：Tassion, Vincent
作者单位：University of Geneva
摘要：We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one arm event at criticality.
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we give a very accurate description of the way the simple exclusion process relaxes to equilibrium. Let P-t denote the semi-group associated the exclusion on the circle with 2N sites and N particles. For any initial condition chi, and for any t >= 4N(2)/9 pi(2) log N, we show that the probability density P-t (chi, center dot) is given by an exponential tilt of the equilibrium measure by the main eigenfunction of the particle system. As 4N(2)/9 pi(2) log N is smaller than the mix...
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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：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：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：Amir, Gideon; Angel, Omer; Benjamini, Itai; Kozma, Gady
作者单位：Bar Ilan University; University of British Columbia; Weizmann Institute of Science
摘要：We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. Under various regularity conditions on the tail of the step distribution, we prove that the diameter grows as n(beta+o(1)), with an explicitly given beta. The growth rate of the aggregate is shown to have three phase transitions, when the walk steps have finite third m...
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作者：Pimentel, Leandro P. R.
作者单位：Universidade Federal do Rio de Janeiro
摘要：In this article, we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times, with scaling exponent 3/2, and we relate its distribution with variational problems involving the Brownian motion process and the Airy(2) process. The proof relies on the relation between Busemann functions and the Burke property for stationary versions of the last-passage percolation mod...
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作者：Mourrat, Jean-Christophe; Otto, Felix
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Max Planck Society
摘要：Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free...
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作者：Duminil-Copin, Hugo; Ioffe, Dmitry; Velenik, Yvan
作者单位：University of Geneva; Technion Israel Institute of Technology
摘要：We consider translationally-invariant percolation models on Z(d) satisfying the finite energy and the FKG properties. We provide explicit upper bounds on the probability of having two distinct clusters going from the end-points of an edge to distance n (this corresponds to a finite size version of the celebrated Burton-Keane [Comm. Math. Phys. 121 (1989) 501-505] argument proving uniqueness of the infinite-cluster). The proof is based on the generalization of a reverse Poincare inequality prov...
