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作者：Li, Xue-Mei
作者单位：University of Warwick
摘要：We study random perturbation to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm 1. We prove that the projections of the solutions to the perturbed equations, converge, after suitable resealing, to a Brownian motion scaled by 8/n(n-1) where n is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal ...
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作者：Tang, Shanjian; Wei, Wenning
作者单位：Fudan University
摘要：This paper is concerned with solution in Holder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic spatial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional Holder spaces for them and give some inequalities among these Holder norms. The existence, uniqueness as well as the regularity of solut...
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作者：Goldschmidt, Christina; Haas, Benedicte
作者单位：University of Oxford; Universite PSL; Universite Paris-Dauphine
摘要：We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power a, independently of the other blocks. Every block then splits randomly into sub-blocks whose relative sizes are distributed according to the so-called dislocation measure. We focus here on the case where alpha < 0. In this case, small blocks split intensively, and so the wh...
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作者：Quas, Anthony; Soo, Terry
作者单位：University of Victoria; University of Kansas
摘要：Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is stochastically dominated by the original measure can be obtained as a monotone factor; that is, the factor map has the property that for each point in the domain, its image under the factor map is coordinatewise smaller than or equal to the original point.
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作者：Cerf, Raphael; Gorny, Matthias
作者单位：Universite Paris Saclay
摘要：We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum S-n of the random variables behaves as in the typical critical generalized Ising Curie Weiss model. The fluctuations are of orde...
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作者：Fontbona, Joaquin; Jourdain, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Inria
摘要：The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale. In the case of (not necessarily reversible) Markov diffusion processes, we use Girsanov theory to explicit the Doob-Meyer decomposition of this submartingale. We deduce a stochastic analogue of the well-known entropy dissipation formula, which is valid for g...
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作者：Avena, Luca; Bolthausen, Erwin; Ritzmann, Christine
作者单位：Leiden University; Leiden University - Excl LUMC; University of Zurich
摘要：We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application we treat such self-avoiding walks in continuous space. The bounds obtained are sharper than those obtained by other methods.
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作者：Chelkak, Dmitry
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any simply connected discrete domain Omega with four marked boundary vertices and are uniform with respect to Omega's which can be very rough, having many fiords and bottlenecks of various widths. Moreover, due to results from [Boundaries of planar graphs, via circle...
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作者：Gonzales-Gargate, Ivan I.; Ruffino, Paulo R.
作者单位：Universidade Estadual de Campinas
摘要：Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order epsilon. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as a goes to zero. An estimate of the rate of convergence is given. These results...
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作者：Hillion, Erwan; Johnson, Oliver
作者单位：University of Luxembourg; Aix-Marseille Universite; University of Bristol
摘要：We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou-Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp-Olkin entropy concavity conjecture.
