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作者：Eckstein, Stephan; Pammer, Gudmund
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT problems numerically. First, we show that AOT problems are stable with respect to perturbations in the marginals, and thus arbitrary AOT problems can be approximated by sequences of linear programs. We further study entropic methods to solve AOT problems. We s...
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作者：Bristiel, Alexandre; Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：We consider activated random walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the nonreversibility of the dynamics and the lack of knowledge on the stationary distribution, we explicitly determine the relaxation time of the process, and prove that separation cutoff is equivalent to the product condition. We also provide sharp estimates on the center and width of the cutoff window. Finally, we illustrate those results by establish...
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作者：Hong, Minhao; Liu, Heguang; Xu, Fangjun
作者单位：Shanghai Maritime University; East China Normal University; East China Normal University
摘要：Under certain mild conditions, limit theorems for additive functionals of some d-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions, subfractional Brownian motions and bi-fractional Brownian motions. To prove these results, we use the method of moments and an enhanced chaining argument. The Gaussian processes under consideration are required to satisfy certain strong local nondeterminism prope...
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作者：Bianchi, Alessandra; Collet, Francesca; Magnanini, Elena
作者单位：University of Padua; University of Verona; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together with a complete characterization of the phase diagram of the model. We borrow tools from statistical mechanics to obtain limit theorems for the edge density. First, we investigate the asymptotic distribution of this quantity, as the graph size tends to infin...
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作者：Cook, Nicholas A.; Dembo, Amir
作者单位：Duke University; Stanford University
摘要：We consider general exponential random graph models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs F-k. Whereas previous work has shown a degeneracy phenomenon in dense ERGMs, we show this can be cured by raising the sufficient statistics to a fractional power. We rigorously establish the naive mean-field approximation for the partition function of the corresponding Gibbs measures, and in case of ferromagnetic models with va...
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作者：Lavenant, Hugo; Zhang, Stephen; Kim, Young-Heon; Schiebinger, Geoffrey
作者单位：Bocconi University; Bocconi University; University of British Columbia
摘要：We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single -cell RNA-sequencing data, which provide high-dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time...
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作者：Djete, Mao fabrice; Touzi, Nizar
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris
摘要：We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding N-agent model. The induced mean field dynamics appear naturally in a form which is not covered by standard McKean-Vlasov stochastic differential equations. We study the corresponding mean field game of mutual holding in the absence of common noise. Our first main result provides an explicit equilibrium of this mean field game, defined by a bang-b...
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作者：Ball, Frank; Sirl, David; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：We investigate final outcome properties of an SIR (susceptible -k infective -k recovered) epidemic model defined on a population of large subcommunities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of com...
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作者：Last, Guenter; Penrose, Mathew d.; Zuyev, Sergei
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; Chalmers University of Technology
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作者：Donoho, David l.; Kipnis, A. lon
作者单位：Stanford University; Reichman University
摘要：Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a p-value, we construct a global test against the joint null using the higher criticism (HC) statistics of these p-values. We calibrate the rare/weak model using parameters controlling the asymptotic distribution of nonnull p-values near zero. We derive a region in the parameter space wh...
