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作者：Zhang, Tusheng
作者单位：University of Manchester
摘要：In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of Dirichlet processes and backward stochastic differential equations play a crucial role.
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作者：Bobkov, Sergey; Madiman, Mokshay
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Yale University
摘要：A concentration property of the functional - log f (X) is demonstrated, when a random vector X has a log-concave density f on R-n. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.
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作者：Coulibaly-Pasquier, Kolehe A.
作者单位：University of Luxembourg
摘要：Using Huisken's results about the mean curvature flow on a strictly convex hypersurface and Kendall-Cranston's coupling, we will build a stochastic process without birth and show that there exists a unique law of such a process. This process has many similarities with the circular Brownian motion studied by Emery and Schachermayer, and Arnaudon. In general this process is not a stationary process; it is linked to some differential equation without initial condition. We will show that this diff...
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作者：Beffara, Vincent; Nolin, Pierre
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); New York University
摘要：We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j + 1)-arm exponents.
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作者：Vershynin, Roman
作者单位：University of Michigan System; University of Michigan
摘要：For probability distributions on R-n, we study the optimal sample size N = N(n, p) that suffices to uniformly approximate the pth moments of all one-dimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain the optimal bound N = O(n(p/2)) for p > 2. This bound goes in the direction of bridging the two recent results: a theorem of Guedon and Rudelson [Adv. Math. 208 (2007) 798-823] which has an extra logarithmic factor in the sample size, and a result of ...
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作者：Amir, Gideon; Angel, Omer; Valko, Benedek
作者单位：Bar Ilan University; University of British Columbia; University of Wisconsin System; University of Wisconsin Madison
摘要：In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in increasing order. Consider the process with the initial configuration where each particle is labeled by its position. It is known that in this case a.s. each particle has an asymptotic speed which is distributed uniformly on [-1, 1]. We study the joint distribution ...
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作者：Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to accommodate other joint laws. In particular, the matricial limits of symmetric circulants and reverse circulants satisfy, respectively, the classical independence and the half independence. The matricial limits of Toeplitz and Hankel matrices do not seem to submi...
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作者：Iyer, Gautam; Novikov, Alexei
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study the dissipation mechanism of a stochastic particle system for the Burgers equation. The velocity field of the viscous Burgers and Navier-Stokes equations can be expressed as an expected value of a stochastic process based on noisy particle trajectories [Constantin and Iyer Comm. Pure Appl. Math. 3 (2008) 330-345]. In this paper we study a particle system for the viscous Burgers equations using a Monte-Carlo version of the above; we consider N copies of the above stochastic flow, each ...
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.
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作者：Sly, Allan
作者单位：Microsoft
摘要：The reconstruction problem on the tree has been studied in numerous contexts including statistical physics, information theory and computational biology. However, rigorous reconstruction thresholds have only been established in a small number of models. We prove the first exact reconstruction threshold in a nonbinary model establishing the Kesten-Stigum bound for the 3-state Potts model on regular trees of large degree. We further establish that the Kesten-Stigum bound is not tight for the q-s...
