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作者：Denis, L; Matoussi, A; Stoica, L
作者单位：Universite Paris Saclay; Le Mans Universite; University of Bucharest
摘要：In this paper we prove L-p estimates (p >= 2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear parabolic PDE.
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作者：Giacomin, G; Toninelli, FL
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
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作者：Blath, J; Mörters, P
作者单位：University of Oxford; University of Bath
摘要：We determine for a super-Brownian motion {X-t : t >= 0} in R-d, d >= 3, the precise gauge function phi such that, almost surely on survival up to time t, [GRAPHICS] improving a result of Barlow, Evans and Perkins about the most visited sites of super-Brownian motion. We also determine upper and lower bounds for the Hausdorff dimension spectrum of thick points refining the multifractal analysis of super-Brownian motion by Taylor and Perkins. The upper bound, conjectured to be sharp, involves a ...
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作者：Gurevich, BM; Tempelman, AA
作者单位：Lomonosov Moscow State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We refine some well-known approximation theorems in the theory of homogeneous lattice random fields. In particular, we prove that every translation invariant Borel probability measure mu on the space X of finite-alphabet configurations on Z(d), d >= 1, can be weakly approximated by Markov measures mu(n) with supp(mu(n)) = X and with the entropies h(mu(n)) --> h(mu). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version...
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作者：Guionnet, A; Mazza, C
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Geneva
摘要：We consider the solution of a nonlinear Kraichnan equation partial derivative H-s(s, t) = integral(s)(t) H(s, u) H(u, t) k(s, u) du, s >= t with a covariance kernel k and boundary condition H( t, t) = 1. We study the long time behaviour of H as the time parameters t, s go to infinity, according to the asymptotic behaviour of k. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linea...
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作者：Duquesne, T; Le Gall, JF
作者单位：Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We investigate the random continuous trees called Levy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted R-trees, which is equipped with the Gromov-Hausdorff distance. To construct Levy trees, we make use of the coding by the height process which was studied in detail in previous work. We then investigate various prob...
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作者：Ben Arous, G; Bogachev, LV; Molchanov, SA
作者单位：New York University; University of Leeds; University of North Carolina; University of North Carolina Charlotte
摘要：We study limiting distributions of exponential sums S-N( t) = Sigma(N)(i=1) e(tXi) as t --> infinity, N --> infinity, where (X-i) are i. i. d. random variables. Two cases are considered: (A) ess sup X-i = 0 and ( B) ess sup X-i = infinity. We assume that the function h(x) = - log P{X-i > x} (case B) or h( x) = - logP{X-i > rho < infinity} ( case A) is regularly varying at 8 with index 1 < rho < infinity(case B) or 0 < rho < infinity(case A). The appropriate growth scale of N relative to t is o...
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作者：Warren, J
作者单位：University of Warwick; University of California System; University of California Berkeley
摘要：A stochastic flow of homeomorphisms of R previously studied by Bass and Burdzy [2] and Hu and Warren [4] is shown to arise in the study of the local times of Brownian motion. This leads to a new proof of the Ray-Knight theorems for the flow via the classical Ray-Knight theorems for Brownian motion.
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作者：Guionnet, A; Maïda, M
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The estimation of various matrix integrals as the size of the matrices goes to infinity is motivated by theoretical physics, geometry and free probability questions. On a rigorous ground, only integrals of one matrix or of several matrices with simple quadratic interaction (called AB interaction) could be evaluated so far (see e.g. [19], [17] or [9]). In this article, we follow an idea widely developed in the physics literature, which is based on character expansion, to study more complex inte...
