-
作者：Bayati, Mohsen; Lelarge, Marc; Montanari, Andrea
作者单位：Stanford University; Inria; Universite PSL; Ecole Normale Superieure (ENS); Stanford University; Stanford University
摘要：We consider a class of nonlinear mappings F-A,F-N in R-N indexed by symmetric random matrices A is an element of R-NxN with independent entries. Within spin glass theory, special cases of these mappings correspond to iterating the TAP equations and were studied by Bolthausen [Comm. Math. Phys. 325 (2014) 333-366]. Within information theory, they are known as approximate message passing algorithms. We study the high-dimensional (large N) behavior of the iterates of F for polynomial functions F,...
-
作者：Craiu, Radu V.; Gray, Lawrence; Latuszynski, Krzysztof; Madras, Neal; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：University of Toronto; University of Minnesota System; University of Minnesota Twin Cities; University of Warwick; York University - Canada
摘要：We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov chain Monte Carlo algorithms.
-
作者：Puha, Amber L.
作者单位：California State University System; California State University San Marcos
摘要：We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded support, it has been shown that standard diffusion scaling yields an identically zero limit. We specify an alternative spatial scaling that produces a nonzero limit. Our model allows for renewal arrivals and i.i.d. processing times satisfying a rapid variat...
-
作者：Reed, Josh; Talreja, Rishi
作者单位：New York University
摘要：We study the G/GI/infinity queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein-Uhlenbeck processes.
-
作者：Jaisson, Thibault; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that very often, only nearly unstable Hawkes processes are able to fit the data properly. By nearly unstable, we mean that the L-1 norm of their kernel is close to unity. We study in this work such processes for which the stability condition is almost violated. Our...
-
作者：Dahmer, Iulia; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：In the Kingman coalescent tree the length of order r is defined as the sum of the lengths of all branches that support r leaves. For r = 1 these branches are external, while for r >= 2 they are internal and carry a subtree with r leaves. In this paper we prove that for any s is an element of N the vector of resealed lengths of orders 1 <= r <= s converges to the multivariate standard normal distribution as the number of leaves of the Kingman coalescent tends to infinity. To this end we use a c...
-
作者：Jacob, Emmanuel; Moerters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Bath
摘要：We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent tau > 2. The average clustering coefficient of the networks converges to a positive lim...
-
作者：Andrieu, Christophe; Tadic, Vladislav B.; Vihola, Matti
作者单位：University of Bristol; University of Jyvaskyla
摘要：We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading t...
-
作者：Auffinger, Antonio; Damron, Michael; Hanson, Jack
作者单位：University of Chicago; Indiana University System; Indiana University Bloomington
摘要：It is an open problem to show that in two-dimensional first-passage percolation, the sequence of finite geodesics from any point to (n, 0) has a limit in n. In this paper, we consider this question for first-passage percolation on a wide class of subgraphs of Z(2): those whose vertex set is infinite and connected with an infinite connected complement. This includes, for instance, slit planes, half-planes and sectors. Writing x(n) for the sequence of boundary vertices, we show that the sequence...
-
作者：Lachieze-Rey, Raphael; Molchanov, Ilya
作者单位：Universite Paris Cite; University of Bern
摘要：We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extension can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed...
