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作者：Dommers, Sander
作者单位：University of Bologna
摘要：We study the metastability of the ferromagnetic Ising model on a random r-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like when the inverse temperature and the number of vertices n is large enough but fixed. The proof is based on the so-called pathwise approach and bounds on the isoperimetric number of random regular graphs.
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作者：Silvestri, Vittoria
作者单位：University of Cambridge
摘要：We study the fluctuations of the outer domain of Hastings-Levitov clusters in the small particle limit. These are shown to be given by a continuous Gaussian process taking values in the space of holomorphic functions on , of which we provide an explicit construction. The boundary values of are shown to perform an Ornstein-Uhlenbeck process on the space of distributions on the unit circle , which can be described as the solution to the stochastic fractional heat equation Equation ID=Equ34 Media...
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作者：Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider the local eigenvalue distribution of large self-adjoint random matrices with centered independent entries. In contrast to previous works the matrix of variances is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, , converges to a diagonal matrix, , ...
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作者：Roch, Sebastien; Sly, Allan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Princeton University
摘要：Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which ...
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作者：Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael
作者单位：University of Pisa; Max Planck Society; Technical University of Berlin
摘要：We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point. As a result, synchronization by noise is proven for a large class of SDE with...
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作者：Kortchemski, Igor
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaym,-Galton-Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.
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作者：Miller, Jason; Sousi, Perla
作者单位：University of Cambridge
摘要：Suppose that X is a simple random walk on for and, for each t, we let consist of those which have not been visited by X by time t. Let be the expected amount of time that it takes for X to visit every site of . We show that there exists and a time as such that the following is true. For (resp. ), the total variation distance between the law of and the law of i.i.d. Bernoulli random variables indexed by with success probability tends to 0 (resp. 1) as . Let be the first time t that . We also sh...
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作者：Lewicka, Marta; Manfredi, Juan J.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We present a probabilistic approach to the obstacle problem for the p-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.
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作者：Rodriguez, Pierre-Francois
作者单位：University of California System; University of California Los Angeles
摘要：We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h. The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold for percolation, a second parameter characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 p...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
摘要：We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker's position, we are able to prove secon...
