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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...
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作者：Hu, Yaozhong; Nualart, David; Song, Jian
作者单位：University of Kansas
摘要：In this paper we introduce the notion of fractional martingale as the fractional derivative of order a of a continuous local martingale, where alpha is an element of (-1/2, 1/2) and we show that it has a nonzero finite variation of order 2/1+2 alpha, under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Levy's characterization theorem for the fractional Brownian motion.
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作者：Morris, Ben
作者单位：University of California System; University of California Davis
摘要：We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then We use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling model in 1973: Suppose the number of cards n is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue t...
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作者：Bloemker, Dirk; Flandoli, Franco; Romito, Marco
作者单位：University of Augsburg; University of Pisa; University of Florence
摘要：The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martin-gale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.
