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作者：Lowther, George
摘要：We consider decompositions of processes of the form Y = f (t, X(t)) where X is a semimartingale. The function f is not required to be differentiable, so Ito's lemma does not apply. In the case where f (t, x) is independent of t, it is shown that requiring f to be locally Lipschitz continuous in x is enough for an Ito-style decomposition to exist. In particular, Y will be a Dirichlet process. We also look at the case where f (t, x) can depend on t, possibly discontinuously. It is shown, under s...
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作者：Pemantle, Robin; Peres, Yuval
作者单位：University of Pennsylvania; Microsoft
摘要：We consider the Ising model on a general tree under various boundary conditions: all plus, free and spin-glass. In each case, we determine when the root is influenced by the boundary values in the limit as the boundary recedes to infinity. We obtain exact capacity criteria that govern behavior at critical temperatures. For plus boundary conditions, an L-3 capacity arises. In particular, on a spherically symmetric tree that has n(alpha)b(n) vertices at level n (up to bounded factors), we prove ...
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作者：Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Consider a Lambda-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number N-t of blocks at any positive time t > 0). We exhibit a deterministic function v: (0, infinity) -> (0, infinity) such that N-t/v(t) -> 1, almost surely, and in L-p for any p >= 1, as t -> 0. Our approach relies on a novel martingale technique.
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作者：Chen, Xia; Li, Wenbo V.; Marcus, Michael B.; Rosen, Jay
作者单位：University of Tennessee System; University of Tennessee Knoxville; City University of New York (CUNY) System; City College of New York (CUNY); University of Delaware; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let {L-t(x); (x, t) is an element of R-1 x R-+(1)} denote the local time of Brownian motion, and alpha(t) := integral(infinity)(-infinity)(L-t(x))(2)dx. Let eta = N(0, 1) be independent of alpha(t). For each fixed t, integral(infinity)(-infinity)(L-t(x+h) - L-t(x))(2) dx - 4ht/h(3/2) L -> (64/3)(1/2) root alpha(t)eta as h -> 0. Equivalently, integral(infinity)(-infinity)(L-t(x+1) - L-t(x))(2) dx - 4t/t(3/4) L -> (64/3)(1/2) root alpha(1)eta as t -> infinity.
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作者：Barlow, M. T.; Deuschel, J-D.
作者单位：University of British Columbia; Technical University of Berlin
摘要：We study a continuous time random walk X in an environment of i.i.d. random conductances mu(e) is an element of [1, infinity). We obtain heat kernel bounds and prove a quenched invariance principle for X. This holds even when E mu(e) = infinity.
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作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda-Guerra identities imply ultrametricity.
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作者：Katalin Marton
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
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作者：Doney, R. A.; Savov, M. S.
作者单位：University of Manchester; Sorbonne Universite
摘要：If X is a stable process of index alpha is an element of (0, 2) whose Levy measure has density cx(-alpha-1) on (0, infinity), and S(1) = sup(0<= 1) X(t), it is known that P(S(1) > x) similar to A alpha-1 x-alpha as x -> infinity and P(S(1) <= x) similar to B alpha(-1) rho(-1) x(alpha rho) as x down arrow 0. [Here rho = (X(1) > 0) and A and B are known constants.] It is also known that S(1) has a continuous density, m say. The main point of this note is to show that m(x) similar to Ax(-(alpha+1...
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作者：Lambert, Amaury
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
摘要：Splitting trees are those random trees where individuals give birth at a constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous Crump-Mode-Jagers (CMJ) process, and is not Markovian unless the lifetime distribution is exponential (or a Dirac mass at {infinity}). Here, we allow the birth rate to be infinite, that is, pairs of birth times and life spans of newborns form a Poisson point process...
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作者：Lebeau, Gilles; Michel, Laurent
作者单位：Universite Cote d'Azur
摘要：We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold (M, g). The proof includes a detailed study of the spectral theory of the associated operator.
