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作者：Goncalves, Patricia; Jara, Milton
作者单位：Universidade de Lisboa
摘要：We show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form where depends on the sign of , are given by a fractional Ornstein-Uhlenbeck process for . When we show that the density fluctuations are tight, in a suitable topology, and that any limit point is an energy solution of the fractional Burgers equation, previously introduced in Gubinelli and Jara (Stoch Partial Differ Equ Anal Comput 1(2):325-350, 2013) in the finite volume setting.
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作者：Buckley, Jeremiah; Feldheim, Naomi
作者单位：University of London; King's College London; Weizmann Institute of Science
摘要：This paper studies the winding of a continuously differentiable Gaussian stationary process f : R. C in the interval [0, T]. We give formulae for the mean and the variance of this random variable. The variance is shown to always grow at least linearly with T, and conditions for it to be asymptotically linear or quadratic are given. Moreover, we show that if the covariance function together with its second derivative are in L2( R), then the winding obeys a central limit theorem. These results c...
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作者：Crisan, Dan; McMurray, Eamon
作者单位：Imperial College London
摘要：In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives...
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作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the lattice. We consider the maximum flows through the edges from a source to a sink in a large cube. In this paper, we show that the ratio of the maximum flow and the size of the source is asymptotic to a constant. This constant is denoted by the flow constant. By the max-flow and min-cut theorem, this is equivalent to a statement about the asymptotic beha...
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作者：Budzinski, Thomas
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We introduce and study a new random surface, which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed by Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The law of the hyperbolic Brownian plane is obtained after biasing the law of the Brownian plane of Curien and Le Gall (J Theoret Probab 27(4):1249-1291, 2014) by an explicit martingale depending on its perimeter and volume processes studied by Curien and Le...
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作者：Collins, Benoit; Dahlqvist, Antoine; Kemp, Todd
作者单位：Kyoto University; Centre National de la Recherche Scientifique (CNRS); University of Cambridge; University of California System; University of California San Diego
摘要：The Brownian motion on the unitary group converges, as a process, to the free unitary Brownian motion as . In this paper, we prove that it converges strongly as a process: not only in distribution but also in operator norm. In particular, for a fixed time , we prove that the unitary Brownian motion has a spectral edge: there are no outlier eigenvalues in the limit. We also prove an extension theorem: any strongly convergent collection of random matrix ensembles independent from a unitary Brown...
