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作者：Baake, Ellen; Cordero, Fernando; Hummel, Sebastian
作者单位：University of Bielefeld
摘要：We consider the mutation-selection differential equation with pairwise interaction (or, equivalently, the diploid mutation-selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph. The formal relation to the forward model is given via duality. To make the tree tractable, we prune branches upon mutations, thus reducing it to its informative parts. The hierarchies inherent in the tree are encoded systematically v...
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作者：Banerjee, Sayan; Budhiraja, Amarjit; Puha, Amber L.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; California State University System; California State University San Marcos
摘要：We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. Since one needs to keep track of the remaining processing times of all jobs in the system in order to describe the evolution, a natural state descriptor for an SRPT queue is a measure valued process in which the state of the system at a given time is the finite nonnegative Borel measure...
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作者：Chen, Hong-Bin
作者单位：New York University
摘要：We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of the two vectors are only assumed to have scaled bounded supports. We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the ...
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作者：Banerjee, Sayan; Olvera-Cravioto, Mariana
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of the model parameters. Interestingly, this power law is heavier than the tail of the limiting in-degree distribution, which goes against the commonly accepted power law hypothesis. This deviation from the power law hypothesis points at the structural difference...
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作者：Guo, Chengkun; Tang, Si; Wei, Ningxi
作者单位：Lehigh University
摘要：We study the recurrence property of one-per-site frog model FM(d, p) on a d-ary tree with drift parameter p is an element of [0, 1], which determines the bias of frogs' random walks. In this model, active frogs move toward the root with probability p or otherwise move to a uniformly chosen child vertex. Whenever a site is visited for the first time, a new active frog is introduced at the site. We are interested in the minimal drift p(d) so that the frog model is recurrent. Using a coupling arg...
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作者：Burdzy, Krzysztof; Kolodziejek, Bartosz; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Warsaw University of Technology; Microsoft
摘要：We study solutions to the stochastic fixed-point equation X =(d) AX + B where the coefficients A and B are nonnegative random variables. We introduce the local dependence measure (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of X. We discuss the relationship of LDM with earlier results on the stochastic fixed-point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.
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作者：Crawford, Nicholas; Rosenthal, Ron
作者单位：Technion Israel Institute of Technology
摘要：The complex Ginibre ensemble is the distribution of an N x N nonHermitian random matrix over C with i.i.d. complex Gaussian entries normalized to have mean zero and variance 1/N. Unlike the Gaussian unitary ensemble, for which the eigenvectors are distributed according to Haar measure on the compact group U (N), independently of the eigenvalues, the geometry of the eigenbases of the Ginibre ensemble are not particularly well understood. In this paper we systematically study properties of eigen...
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作者：Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas
作者单位：McGill University; University of Oxford
摘要：We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in d dimensions. The model consists of N particles undergoing dyadic branching Brownian motion with rate 1. At a branching event, the number of particles is kept equal to N by removing the particle located furthest away from the barycenter. To prove the invariance principle, a key step is to establish Harris recurrence for the process viewed from its barycenter.
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作者：Bakhtin, Yuri; Chen, Hong-Bin; Pajor-Gyulai, Zsolt
作者单位：New York University
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作者：Lachieze-Rey, Raphael; Peccati, Giovanni; Yang, Xiaochuan
作者单位：Universite Paris Cite; University of Luxembourg; Brunel University
摘要：We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the order one-that we evaluate and compare at two different scales-and are specifically tailored for studying the Gaussian fluctuations of sequences of geometric functionals displaying a form of weak stabilization-see Penrose and Yukich (Ann. Appl. Probab. 11 (2001)...
