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作者：Fontes, L. R. G.; Mathieu, P.
作者单位：Aix-Marseille Universite
摘要：We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform distribution. We show how these processes arise, in a particular instance, as scaling limits of the trap model in the complete graph, and subsequently derive aging results for those models in this context.
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作者：Flury, Markus
作者单位：University of Zurich
摘要：We investigate the free energy of nearest-neighbor random walks on Z(d), endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions d >= 4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.
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作者：Campanino, Massimo; Ioffe, Dmitry; Velenik, Yvan
作者单位：University of Bologna; University of Geneva
摘要：We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional chains of irreducible objects. Statistics of local observables, for example, displacement, over such chains obey classical limit laws, and our construction leads to an effective random walk representation of percolation clusters. The results include a derivatio...
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作者：Nachmias, Asaf; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 denote the largest connected component of the critical Erdos-Renyi random graph G(n, 1/n). We show that, typically, the diameter of C-1 is of order n(1/3) and the mixing time of the lazy simple random walk on C-1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald. These results extend to clusters of size n(2/3) of p-bond percolation on any d-regular n-vertex graph where such clusters exist, provided that p(d-1) <= 1 + O(n(-1/3)).
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作者：Helton, J. William; Lasserre, Jean B.; Putinar, Mihai
作者单位：University of California System; University of California San Diego; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Santa Barbara
摘要：We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure mu has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain conditional triangularity property of the orthogonal polynomials associated with mu.
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作者：Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of ...
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance Must be bounded has an explicit formula that makes it possible to carry out the program more easily. As an application, we derive a general CLT for functions that are obtained as combinations of many local contributions,...
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作者：Gouere, Jean-Baptiste
作者单位：Universite de Orleans
摘要：We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if E(R-d) is finite, where R denotes the radius of the balls around Poisson points and d denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.
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作者：Pittel, Boris
作者单位：University System of Ohio; Ohio State University
摘要：Consider a uniformly random regular graph of a fixed degree d >= 3, with it vertices. Suppose that each edge is open (closed), with probability p(q = 1 - p), respectively. In 2004 Alon, Benjamini and Stacey proved that p* = (d - 1)(-1) is the threshold probability for emergence of a giant component in the subgraph formed by the open edges. In this paper we show that the transition window around p* has width roughly of order n(-1/3). More precisely, suppose that p = p(n) is such that omega := n...
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作者：Karatzas, Ioannis; Zamfirescu, Ingrid-Mona
作者单位：Columbia University; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities.
