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作者：Ferrari, Pablo A.; Olla, Stefano
作者单位：University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of Buenos Aires; Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France; Gran Sasso Science Institute (GSSI)
摘要：We study the fluctuations in equilibrium for a dynamics of rods with random length. This includes the classical hard rod elastic collisions, when rod lengths are constant and equal to a positive value. We prove that in the diffusive space-time scaling, an initial fluctuation of density of particles of velocity v, after recentering on its Euler evolution, evolve randomly shifted by a Brownian motion of variance D(v).
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作者：Agresti, Antonio; Hieber, Matthias; Hussein, Amru; Saal, Martin
作者单位：Institute of Science & Technology - Austria; Technical University of Darmstadt; University of Kaiserslautern
摘要：In this paper, we introduce and study the primitive equations with non- isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in H1 where the noise is considered in both the ...
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作者：Chatterjee, Sabyasachi; Dey, Partha S.; Goswami, Subhajit
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Tata Institute of Fundamental Research (TIFR)
摘要：We prove a central limit theorem for the Horvitz-Thompson estimator based on the Gram-Schmidt walk (GSW) design, recently developed in Harconsider the version of GSW design, which uses a randomized pivot order. We deduce our result under very mild assumptions involving only the problem parameters, such as the (sum) potential outcome vector and the covariate matrix. As a very important consequence of our analysis, we obtain the precise limiting variance of the estimator in terms of these parame...
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作者：Englander, Janos; Iacobelli, Giulio; Pete, Gabor; Ribeiro, Rodrigo
作者单位：University of Colorado System; University of Colorado Boulder; Universidade Federal do Rio de Janeiro; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Budapest University of Technology & Economics; University of Denver
摘要：We study the tree builder random walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time n , she adds a leaf to her current vertex with probability pn = n-gamma , gamma is an element of ( 2 / 3 , 1], then moves to a uniform random neighbor on the possibly modified tree. We show that the tree process at its growth times, after a random finite number of steps, can be coupled to be identical to the Barab & aacute;si-Albert preferential attachment t...
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作者：Forsstrom, Malin p.; Lenells, Jonatan; Viklund, Fredrik
作者单位：Chalmers University of Technology; Royal Institute of Technology
摘要：We consider the 4D fixed length lattice Higgs model with Wilson action for the gauge field and structure group Zn. We study Wilson line observables in the strong coupling regime and compute their asymptotic behavior with error estimates. Our analysis is based on a high-temperature representation of the lattice Higgs measure combined with Poisson approximation. We also give a short proof of the folklore result that Wilson line (and loop) expectations exhibit perimeter law decay whenever the Hig...
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作者：Duffie, Darrell; Qiao, Lei; Sun, Yeneng
作者单位：Stanford University; Shanghai University of Finance & Economics; National University of Singapore
摘要：Continuous-time random matching with a large (continuum) population is widely exploited in the literature, but has not had a rigorous formulation, nor a demonstration of its key assumed properties. This paper provides the first probabilistic foundation for this approach by presenting a mathematical model of continuous-time random matching and showing its existence and properties. The agents' types, which can change due to random matching and random mutation, form a continuum of independent con...
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作者：Dianetti, Jodi
作者单位：University of Rome Tor Vergata
摘要：This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some structural conditions which are related to the submodularity of the underlying mean field game and are a sort of opposite version of the well known Lasry-Lions monotonicity. By reformulating the representative player minimization problem via the stochastic maximum p...
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作者：Armentano, Diego; Azais, Jean-m arc; Leon, Jose afael
作者单位：Universidad de la Republica, Uruguay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universidad de la Republica, Uruguay
摘要：Let X() be a random field from R-D to R-d, where D >= d. We study the level set X-1(u), where u is an element of R-d. Specifically, we provide a weak condition for this level set to be rectifiable. Next, we establish the Kac-Rice formula to compute the (D-d)-dimensional Hausdorff measure. Our results extend previous work, particularly in the non-Gaussian case where we obtain a very general result. We conclude with several extensions and examples of applications, including functions of Gaussian...
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作者：Beh, Jason; Shadmi, Yonatan; Simatos, Florian
作者单位：Universite de Toulouse; National Office for Aerospace Studies & Research (ONERA); Technion Israel Institute of Technology; Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); National Office for Aerospace Studies & Research (ONERA)
摘要：We study two adaptive importance sampling schemes for estimating the probability of a rare event in the high-dimensional regime d - oc with d the dimension. The first scheme is the prominent cross-entropy (CE) method, and the second scheme, motivated by recent results, uses as auxiliary distribution a projection of the optimal auxiliary distribution on a lower-dimensional subspace. In these schemes, two samples are used: the first one to learn the auxiliary distribution and the second one, dra...
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作者：Ning, Ning
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Markov chain Monte Carlo (MCMC) algorithms have played a significant role in statistics, physics, machine learning and others, and they are the only known general and efficient approach for some high-dimensional problems. The random walk Metropolis (RWM) algorithm as the most classical MCMC algorithm, has had a great influence on the development and practice of science and engineering. The behavior of the RWM algorithm in high-dimensional problems is typically investigated through a weak conve...
