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作者：Budhiraja, Amarjit; Friedlander, Eric
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider a rate control problem for an N-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state simultaneously. Such models have been proposed for large communication systems (e.g., ad hoc wireless networks) but are also suitable for other settings such as chemical-reaction networks. An associated diffusion control problem is presented and we show that the value func...
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作者：Benaim, Michel; Cloez, Bertrand; Panloup, Fabien
作者单位：Institut Agro; Montpellier SupAgro; Universite de Montpellier; INRAE; Universite d'Angers
摘要：As a continuation of a recent paper, dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ...
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作者：Duchamps, Jean-Jil; Lambert, Amaury
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Institut National de la Sante et de la Recherche Medicale (Inserm); Centre National de la Recherche Scientifique (CNRS); Universite PSL; College de France
摘要：Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure (infinitely-many-allele model) on the skeleton of the tree. The partition of the boundary into distinct alleles is the so-called allelic partition. In this paper, we are interested in the infinite trees generated by supercritical, possibly time-inhomogeneous, binary branching pr...
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作者：Leon, Jose R.; Samson, Adeline
作者单位：Universidad de la Republica, Uruguay; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; University of Central Venezuela
摘要：The FitzHugh-Nagumo is a well-known neuronal model that describes the generation of spikes at the intracellular level. We study a stochastic version of the model from a probabilistic point of view. The hypoellipticity is proved, as well as the existence and uniqueness of the stationary distribution. The bi-dimensional stochastic process is beta-mixing. The stationary density can be estimated with an adaptive non-parametric estimator. Then we focus on the distribution of the length between succ...
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作者：van der Hoorn, Pim; Olvera-Cravioto, Mariana
作者单位：Northeastern University; University of California System; University of California Berkeley
摘要：We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the in-degree and out-degree is finite, we show that the distance grows logarithmically in the size of the graph. In contrast with the undirected case, this can happen even when the variance of the degrees is infinite. The main tool in the analysis is a new coupling b...
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作者：Del Moral, P.; Tugaut, J.
作者单位：Universite de Bordeaux
摘要：The ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov-type particle interpretation of the Kalman-Bucy diffusions. In contrast to more conventional particle filters and nonlinear Markov processes, these models are designed in terms of a diffusion process with a diffusion matrix that depends on particle...
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作者：Xu, Liping
作者单位：Sorbonne Universite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials [gamma epsilon ( -1, 0)] using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the class of all weak solutions, assuming only that the initial condition has a finite entropy and a finite moment of sufficiently high order. We also consider the Nanbu N-stochastic particle system, which approximates the weak solution. We use a probabilistic...
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作者：Krishnan, Arjun; Quastel, Jeremy
作者单位：University of Rochester; University of Toronto
摘要：The free-energy fluctuations of the discrete directed polymer in 1 + 1 dimensions is conjecturally in the Tracy-Widom universality class at all finite temperatures and in the intermediate disorder regime. Seppalainen's log-gamma polymer was proven to have GUE Tracy-Widom fluctuations in a restricted temperature range by Borodin, Corwin and Remenik [Comm. Math. Phys. 324 (2013) 215-232]. We remove this restriction, and extend this result into the intermediate disorder regime. This result also i...
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作者：Li, Yao
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：We consider a stochastic energy exchange model that models the 1-D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of the nonequilibrium steady state (NESS) and, furthermore, the polynomial speed of convergence to the NESS. Our result shows that the asymptotic properties of this model and its deterministic dynamical system origin are consistent. The proof uses a new technique called the induced chain method. We partition the state...
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作者：Bolley, Francois; Chafai, Djalil; Fontbona, Joaquin
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：We study the long-time behavior of the dynamics of interacting planar Brownian particles, confined by an external field and subject to a singular pair repulsion. The invariant law is an exchangeable Boltzmann-Gibbs measure. For a special inverse temperature, it matches the Coulomb gas known as the complex Ginibre ensemble. The difficulty comes from the interaction which is not convex, in contrast with the case of one-dimensional log-gases associated with the Dyson Brownian motion. Despite the ...
