-
作者：Croydon, David A.; Fukushima, Ryoki; Junk, Stefan
作者单位：Kyoto University; University of Tsukuba; Tohoku University
摘要：We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a discontinuous scale function, as given by a two-sided stable subordinator. Corresponding to intervals of low conductance in the discrete model, the discontinuities in the scale function act as barriers off which the limiting process reflects for some time befor...
-
作者：Bayraktar, Erhan; Chakraborty, Suman; Wu, Ruoyu
作者单位：University of Michigan System; University of Michigan; Uppsala University; Iowa State University
摘要：We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon mean field system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness, continuity a...
-
作者：Hermon, Jonathan; Olesker-Taylor, Sam
作者单位：University of British Columbia; University of Warwick
摘要：Consider the random Cayley graph of a finite Abelian group G with re-spect to k generators chosen uniformly at random, with 1 << log k << log |G|. Draw a vertex U <^> Unif(G).We show that the graph distance dist(id, U) from the identity to U con-centrates at a particular value M, which is the minimal radius of a ball in Zk of cardinality at least |G|, under mild conditions. In other words, the distance from the identity for all but o(|G|) of the elements of G lies in the interval [M -o(M), M +...
-
作者：Popovic, Lea; Veber, Amandine
作者单位：Concordia University - Canada; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the p...
-
作者：Barbour, A. D.; Ross, Nathan; Zheng, Guangqu
作者单位：University of Zurich; University of Melbourne; University of Liverpool
摘要：We develop a general approach to Stein's method for approximating a random process in the path space D([0, T] -> Rd) by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as integrals with respect to an underlying point process, de-riving a general quantitative Gaussian approximation. The error bound is ex-pressed in terms of couplings of the original process to processes generated from the reduced Palm measures associated with t...
-
作者：Kortchemski, Igor; Marzouk, Cyril
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We first establish new local limit estimates for the probability that a non -decreasing integer-valued random walk lies at time n at an arbitrary value, encompassing in particular large deviation regimes on the boundary of the Cramer zone. This enables us to derive scaling limits of such random walks conditioned by their terminal value at time n in various regimes. We believe both to be of independent interest. We then apply these results to obtain in-variance principles for the Lukasiewicz pa...
-
作者：Leme, Renato Paes; Schneider, Jon
作者单位：Alphabet Inc.; Google Incorporated
摘要：We consider the problem of computing with many coins of unknown bias. We are given access to samples of n coins with unknown biases p1, . . . , pn and are asked to sample from a coin with bias f (p1, ... , pn) for a given function f : [0, 1]n -> [0, 1]. We give a complete characterization of the functions f for which this is possible. As a consequence, we show how to extend various combinatorial sampling procedures (most notably, the classic Sampford sampling for k-subsets) to the boundary of ...
-
作者：Zhang, Deng
作者单位：Shanghai Jiao Tong University
摘要：We study the stochastic nonlinear Schrodinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy -critical cases. For general initial data, we prove the global well-posedness of solutions in both mass-critical and energy-critical cases. We also prove the rescaled scattering behavior of global solutions in the spaces L-2, H-1 as well as the pseudo-conformal space for dimensions d >= 3 in the case of finite global quadratic variation of noise. Fur...
-
作者：Last, Guenter; Otto, Moritz
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Aarhus University
摘要：We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach of Hofer-Temmel (Electron. J. Probab. 24 (2019) 1-22) and Hofer-Temmel and Houdebert (Stochastic Process. Appl. 129 (2019) 3922-3940) we will use this to couple two finite Gibbs processes with different boundary conditions. As one application we will establish Poisson approximation of point processes derived from certain infinite volume Gibbs processes ...
-
作者：Ararat, Cagin; Ma, Jin; Wu, Wenqian
作者单位：Ihsan Dogramaci Bilkent University; University of Southern California
摘要：In this paper, we establish an analytic framework for studying set -valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of inverse operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. ...
