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作者：Cotsakis, Ryan; Di Bernardino, Elena; Duval, Celine
作者单位：Universite Cote d'Azur; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The excursion set of a C2 smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to observations at discrete points in space. It has been reported that for specific regular lattices of points in dimensions 2 and 3, the usual approximation of the surface area of the excursions does not converge when the lattice becomes dense in the domain of observatio...
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作者：Drewitz, Alexander; Gallo, Gioele; Prevost, Alexis
作者单位：University of Cologne; University of Geneva
摘要：The study of Gaussian free field level sets on supercritical Galton- Watson trees has been initiated by Ab & auml;cherli and Sznitman in 2018. By means of entirely different tools, we continue this investigation and generalize their main result on the positivity of the associated percolation critical parameter h* to the setting of arbitrary supercritical offspring distribution and random conductances. In our setting, this establishes a rigorous proof of the physics literature mantra that posit...
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作者：Cox, Alexander M. G.; Kallblad, Sigrid; Larsson, Martin; Svaluto-Ferro, Sara
作者单位：University of Bath; Royal Institute of Technology; Carnegie Mellon University; University of Verona
摘要：We consider a class of stochastic control problems where the state process is a probability measure -valued process satisfying an additional martingale condition on its dynamics, called measure -valued martingales (MVMs). We establish the classical results of stochastic control for these problems: specifically, we prove that the value function for the problem can be characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to pro...
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作者：Hundrieser, Shayan; Klatt, Marcel; Munk, Axel
作者单位：University of Gottingen
摘要：For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian process and that the empirical entropic optimal transport value is asymptotically normal. The results are valid for a large class of cost functions and generalize distributional limits for empirical entropic optimal transport quantities on finite spaces. Our pro...
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作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：Consider the Monge-Kantorovich problem of transporting densities rho(0) to rho(1) on R-d with a strictly convex cost function. A popular regularization of the problem is the one-parameter family called the entropic cost problem. The entropic cost K-h, h> 0, is significantly faster to compute and hK(h) is known to converge to the optimal transport cost as h goes to zero. We are interested in the rate of convergence. We show that the difference between K-h and 1/ h times the optimal cost of tran...
