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作者：Pinelis, Iosif
作者单位：Michigan Technological University
摘要：It is shown that, for any given p >= 5, A > 0 and B > 0, the exact upper bound on is an element of vertical bar Sigma X-i vertical bar(p) over all independent zero-mean random variables (r.v.'s) X-1, ..., X-n such that Sigma is an element of X-i(2) = B and Sigma is an element of vertical bar X-i vertical bar(p) = A equals c(p) is an element of vertical bar Pi(lambda) - lambda vertical bar(p), where (lambda, c) is an element of (0, infinity)(2) is the unique solution to the system of equations ...
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作者：Eckhoff, Maren; Kyprianou, Andreas E.; Winkel, Matthias
作者单位：University of Bath; University of Oxford
摘要：Consider a supercritical superdiffusion (X-t)(t >= 0) on a domain D subset of R-d with branching mechanism (x, z) bar right arrow -beta(x)z + alpha(x)z(2) + integral((0, infinity))(e(-zy) - 1 + zy)Pi(x, dy). The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. We use this decomposition to derive the strong law of large numbers (SLLN) for a wide class of superdiffusions from the corresponding result for branching...
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作者：Harangi, Viktor; Virag, Balint
作者单位：University of Toronto
摘要：A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum lambda(min) of the spectrum of the adjacency matrix. To complement this result we use random eigenvectors to gain lower bounds in the vertex-transitive case. For example, we prove that the independence ratio of a 3-regular transitive graph is at least q = 1/2 - 3/4 pi arccos (1-lambda(min)/4). The same bound holds for infinite transitive graphs: we construct factor of i.i.d. independen...
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作者：Lyons, Terry; Ni, Hao
作者单位：University of Oxford
摘要：The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor algebra and is an essential object in rough path theory. The expected signature of a stochastic process plays a similar role to that played by the characteristic function of a random variable. In [Chevyrev (2013)], it is proved that under certain boundednes...
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作者：Kleptsyn, Victor; Kurtzmann, Aline
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we construct a counterexample to a question by Cantelli, asking whether there exists a nonconstant positive measurable function phi such that for i.i.d. r.v. X, Y of law N(0, 1), the r.v. X + phi(X) . Y is also Gaussian. This construction is made by finding an unusual solution to the Skorokhod embedding problem (showing that the corresponding Brownian transport, contrary to the Root barrier, is not unique). To find it, we establish some sufficient conditions for the continuity o...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppaelaeinen, Timo; Yilmaz, Atilla
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Bogazici University
摘要：We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit of quenched polymer measures. We prove this limit for the exactly solvable log-gamma polymer, as a consequence of almost sure limits of ratios of partition functions. These limits of ratios give the Busemann functions of the log-gamma polymer, and furnish cen...
