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作者：Bramson, Maury; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these rec...
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作者：Hochman, Michael
作者单位：Hebrew University of Jerusalem
摘要：For arrays (S(i, j))(1 <= i <= j) of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S(l, n))(n=1)(infinity) can be bounded in terms of a measure of the mean subadditivity of the process (S(i, j))(1 <= i <= j). We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon-MacMillan-Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.
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作者：Reinert, Gesine; Roellin, Adrian
作者单位：University of Oxford; National University of Singapore
摘要：In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide ...
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作者：Balogh, Jozsef; Bollobas, Bela; Morris, Robert
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Cambridge; University of Memphis; University of Cambridge
摘要：By bootstrap percolation we mean the following deterministic process on a graph G. Given a set A of vertices infected at time 0, new vertices are subsequently infected, at each time step, if they have at least r is an element of N previously infected neighbors. When the set A is chosen at randorn, the main aim is to determine the critical probability p(c)(G, r) at which percolation (infection of the entire graph) becomes likely to occur. This bootstrap process has been extensively studied on t...
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作者：Mountford, Thomas; Schonmann, Roberto H.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of California System; University of California Los Angeles
摘要：We study the threshold theta contact process on Z(d) with infection parameter lambda. We show that the critical point lambda(c), defined as the threshold for survival starting from every site occupied, vanishes as d -> infinity. This implies that the threshold theta voter model on Z(d) has a nondegenerate extremal invariant measure, when d is large.
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作者：Howitt, Chris; Warren, Jon
作者单位：University of Warwick
摘要：Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice Z. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random proportion distributed according to some specified probability measure on [0, 1] and dividing the mass in that proportion. One part then moves to each of the two adjacent sites. This paper considers a continuous analogue of this evolution, which may be described by means of a st...
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作者：Wang, Dong
作者单位：Brandeis University
摘要：We solve the largest sample eigenvalue distribution problem in the rank I spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge. We observe a phase change phenomenon similar to that in the complex case, and prove that the new distribution at the phase change point is the GOE Tracy-Widom distribution.
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作者：Caravenna, Francesco; Deuschel, Jean-Dominique
作者单位：University of Padua; Technical University of Berlin
摘要：We consider a random field phi: {1,..., N} -> R with Laplacian interaction of the form Sigma(i) V(Delta phi(i)), where Delta is the discrete Laplacian and the potential V(.) is symmetric and uniformly strictly convex. The pinning model is defined by giving the field a reward epsilon >= 0 each time it touches the x-axis, OF that plays the role of a defect line. It is known that this model exhibits a phase transition between a delocalized regime (epsilon < epsilon(c)) and a localized one (epsilo...
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作者：Lember, Jueri; Matzinger, Heinrich
作者单位：University of Tartu; University System of Georgia; Georgia Institute of Technology
摘要：Let L-n be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length n, We prove that the order of the standard deviation of L-n is root n, provided the parameter of the Bernoulli variables is small enough. This validates Waterman's conjecture in this situation [Philos. Trans. R. Soc. Lond. Ser B 344 (1994) 383-390]. The order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306-315], however, is different.
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作者：Barbu, Viorel; Da Prato, Giuseppe; Roeckner, Michael
作者单位：Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Bielefeld; Purdue University System; Purdue University
摘要：This paper addresses the existence and uniqueness of strong solutions to stochasic porous media equations dX - Delta Psi(X)dt = B(X)dW(t) in bounded domains of R-d with Dirichlet boundary conditions. Here Psi is a maximal monotone graph in R x R (possibly multivalued) with the domain and range all of R. Compared with the existing literature on stochastic porous media equations, no growth condition on Psi is assumed and the diffusion coefficient Psi might be multivalued and discontinuous. The l...
