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作者：Borga, Jacopo; Slivken, Erik
作者单位：University of Zurich; Universite PSL; Universite Paris-Dauphine
摘要：We describe the limit (for two topologies) of large uniform random square permutations, that is, permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square permutations. Building on that, we first describe the global behavior by showing that these permutations have a permuton limit which can be described by a random rectangle. We also explore fluctuations about this random rectangle, which we can describe through...
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作者：Banerjee, Sayan; Mukherjee, Debankur
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University System of Georgia; Georgia Institute of Technology
摘要：Consider a system of N parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate.(N). When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (Math. Oper. Res. 43 (2018) 867-886) identified a novel limiting diffusion process that arises as the weak-limit of the appropriately scaled occupancy measure of the syste...
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作者：Fromm, Alexander; Imkeller, Peter
作者单位：Friedrich Schiller University of Jena; Humboldt University of Berlin
摘要：We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled forward-backward stochastic differential equation (FBSDE) and concentrate on showing existence and uniqueness of solution processes to this FBSDE. We use the method of decoupling fields for strongly coupled, multi-dimensional and possibly non-Lipschitz systems as the central technique in conducting the proofs.
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作者：Bank, Peter; Besslich, David
作者单位：Technical University of Berlin
摘要：In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-sigma-fields as a flexible tool to model information flow in such situations. The possibilities of this approach are illustrated first in a very simple linear stochastic control problem and then in a...
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作者：Ahlberg, Daniel; Deijfen, Maria; Hoffman, Christopher
作者单位：Stockholm University; University of Washington; University of Washington Seattle
摘要：The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane Z x Z(+), and prove that coexistence of two types starting o...
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作者：Labbe, Cyril; Lacoin, Hubert
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider the simple exclusion process with k particles on a segment of length N performing random walks with transition p > 1/2 to the right and q = 1 - p to the left. We focus on the case where the asymmetry in the jump rates b = p - q > 0 vanishes in the limit when N and k tend to infinity, and obtain sharp asymptotics for the mixing times of this sequence of Markov chains in the two cases where the asymmetry is either much larger or much smaller than (log k)/N. We show that in the former...
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作者：Garavaglia, Alessandro; van der Hofstad, Remco; Litvak, Nelly
作者单位：Eindhoven University of Technology; University of Twente
摘要：PageRank is a well-known algorithm for measuring centrality in networks. It was originally proposed by Google for ranking pages in the World Wide Web. One of the intriguing empirical properties of PageRank is the so-called 'power-law hypothesis': in a scale-free network, the PageRank scores follow a power law with the same exponent as the (in-)degrees. To date, this hypothesis has been confirmed empirically and in several specific random graphs models. In contrast, this paper does not focus on...
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作者：Dolera, Emanuele; Favaro, Stefano
作者单位：University of Pavia; University of Turin
摘要：This paper contributes to the study of the random number K-n of blocks in the random partition of {1, ..., n} induced by random sampling from the celebrated two parameter Poisson-Dirichlet process. For any alpha is an element of (0, 1) and theta > -alpha Pitman (Combinatorial Stochastic Processes (2006) Springer, Berlin) showed that n(-alpha) K-n ->(a.s.) S-alpha,S-theta as n -> +infinity, where the limiting random variable, referred to as Pitman's alpha-diversity, is distributed according to ...
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作者：Yan, Jun
作者单位：Stanford University
摘要：By extending (Adv. Math. 299 (2016) 396-450), we present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces. Previous research on nonlinear large deviations has only focused on random variables supported on {-1, +1}(n), and accordingly we build theory for random variables with general distributions, increasing flexibility in the applications. As examples, we compute the large deviation rate functions for ...
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作者：Buijsrogge, Anne; Dupuis, Paul; Snarski, Michael
作者单位：University of Twente; Brown University
摘要：In this paper we study the performance of splitting algorithms, and in particular the RESTART method, for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point during some long time interval [0, T]. We show that, in contrast to alternatives such as importance sampling, the decay rate of the second moment does not degrade as T -> infinity. In the course of the analysis we develop some related large deviation estimates that apply when the time ...
