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作者：Muirhead, Stephen; Rivera, Alejandro; Vanneuville, Hugo; Kohler-Schindler, Laurin
作者单位：University of London; Queen Mary University London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the 'FKG inequality'), and hence many classical arguments in percolation theory do not apply. More precisely, we consider a smooth stationary centred planar Gaussian field f and, given a level l epsilon R, we study the connectivity properties of the excursion set {f >= -l}. We prove th...
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作者：Benjamini, Itai; Tov, Hagai Helman; Zhukovskii, Maksim
作者单位：Weizmann Institute of Science
摘要：We observe the outcome of the discrete time noisy voter model at a single vertex of a graph. We show that certain pairs of graphs can be distinguished by the frequency of repetitions in the sequence of observations. We prove that this statistic is asymptotically normal and that it distinguishes between (asymptotically) almost all pairs of finite graphs. We conjecture that the noisy voter model distinguishes between any two graphs other than stars.
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作者：Bobkov, Sergey G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Upper pointwise bounds are considered for convolution of bounded densities in terms of the associated Laplace and Legendre transforms. Applications of these bounds are illustrated in the central limit theorem with respect to the Renyi divergence.
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作者：Comets, Francis; Dalmau, Joseba; Saglietti, Santiago
作者单位：Universite Paris Cite; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of Z and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. and heavy tailed, and where each block sticks to the interface at the first point of contact with probability p (otherwise, it falls straight down until it lands on a bloc...
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作者：Halberstam, Noah; Hutchcroft, Tom
作者单位：University of Cambridge; California Institute of Technology
摘要：We prove that if (X-n)(n >= 0) is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then (X-n)(n >= 0) has infinitely many cut times almost surely. This condition applies in particular to any graph of spectral dimension strictly larger than 2. In fact, our proof applies to general (possibly nonreversible) Markov chains satisfying a similar decay condition for the Green's function that is sharp for birth-death chains. We deduce...
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作者：Kosygina, Elena; Mountford, Thomas; Peterson, Jonathon
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
摘要：We use generalized Ray-Knight theorems, introduced by B. Toth in 1996, together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusively scaled self-interacting random walks (SIRW) to Brownian motions perturbed at extrema (BMPE). Toth's work studied two classes of SIRWs: asymptotically free and polynomially self-repelling walks. For both classes Toth has shown, in particular, that the d...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W12+epsilon,loc, and the drift in a Morrey class containing Ld. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.
