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作者：Aghajani, Reza; Ramanan, Kavita
作者单位：University of California System; University of California San Diego; Brown University
摘要：We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by N identical servers in a first-come-first-serve manner. We introduce a two-component infinite-dimensional Markov process that serves as a diffusion model for this network, in the regime where the number of servers goes to infinity and the load on the network scales as 1 - beta N-1/2 + o(N-1/2) f...
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作者：Banerjee, Sayan; Mukherjee, Debankur
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
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 A(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) established that in the Halfin-Whitt regime where (N - lambda(N))/root N -> beta > 0 as N -> infinity, appropriately scaled occupancy...
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作者：Hwang, Jong Yun; Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Royal Institute of Technology
摘要：We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdos-Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable condition on the sparsity, we also prove that the limiting distribution of the rescaled, shifted extremal eigenvalues is given by the GOE Tracy-Widom law with an explicit formula on the deterministic shift of the spectral edge. For the biadjacency matrix...
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作者：Li, Pei-Sen; Yang, Xu; Zhou, Xiaowen
作者单位：Renmin University of China; North Minzu University; Concordia University - Canada
摘要：In this paper, we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process: X-t = x + integral(t)(0) gamma 0(X-s)ds + integral(t)(0)integral(gamma 1(Xs-))(0) W(ds, du) +integral(t)(0)integral(infinity)(0)integral(gamma 2(Xs-))(0) z (N) over tilde (ds, dz, du) where W(dt, du) and (N) over tilde (ds, dz, du) denote a Gaussian white noise and an independent compensated spectrally positive Poisson...
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let x(1 ), . . . , x(n) be independent random vectors of a common p-dimensional normal distribution with population correlation matrix R-n . The sample correlation matrix (R) over cap (n) = ((r) over cap (ij))(pxp) is generated from x(1) , . . . . ,x(n) such that (r) over cap (ij) is the Pearson correlation coefficient between the ith column and the jth column of the data matrix (x(1 ), . . . , x(n))'. The matrix (R) over cap (n) is a popular object in multivariate analysis and it has many con...
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作者：Kortchemski, Igor; Richier, Loic
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are interested in the structure of large Bienayme-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index alpha = 1. In stark contrast to the case alpha is an element of (1, 2], we show that a condensation phenomenon occurs: in such trees, one vertex with macroscopic degree emerges (see Figure 1). To this end, we establish limit theorems for centered downwards skip-free random walks whose steps are in the domain ...
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作者：Aghajani, Reza; Ramanan, Kavita
作者单位：University of California System; University of California San Diego; Brown University
摘要：Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent and identically distributed service times are assigned to the shortest queue among a subset of d queues chosen uniformly at random, and leave the network on completion of service. Prior work on dynamical properties of this model has focused on the case of ex...
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作者：Bank, Peter; Dolinsky, Yan
作者单位：Technical University of Berlin; Hebrew University of Jerusalem; Monash University
摘要：We study super-replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market models the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result derives nontrivial scaling limits of super-replication prices for binomial models with small fixed cos...
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作者：Bovier, Anton; Coquille, Loren; Smadi, Charline
作者单位：University of Bonn; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); INRAE; Universite Paris Cite
摘要：We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0, 1, . . . , L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fit...
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作者：Tameling, Carla; Sommerfeld, Max; Munk, Axel
作者单位：University of Gottingen
摘要：We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a delta method for nonlinear derivatives. A careful calibration of the norm on the space of probability measures is needed in order to combine differentiability and weak convergence of the underlying empirical process. Based on this, we provide a sufficient an...
