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作者：Jackson, Joe
作者单位：University of Texas System; University of Texas Austin
摘要：Using probabilistic methods, we establish a priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity, which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward backward stochastic differential equations.
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作者：Deb, Nabarun; Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
作者单位：Columbia University; Harvard University
摘要：In this paper we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising models on lattices, and mean-field type Ising models (Erdos-Renyi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising models, and demonstrate the beneficial behavior of criticality in detection of strictly lower signals. As a by-product of our proof technique, we develo...
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作者：Deligiannidis, George; de Bortoli, Valentin; Doucet, Arnaud
作者单位：University of Oxford
摘要：We establish that the iterates of the iterative proportional fitting procedure, also known as Sinkhorn's algorithm and commonly used to solve entropy-regularised optimal transport problems, are stable w.r.t. perturbations of the marginals, uniformly in time. Our result is quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we establish a quantitative stability result for Schrodinger bridges.
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作者：Bou-Rabee, Ahmed
作者单位：University of Chicago
摘要：We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counter-examples that convergence may not occur in general. A corollary of our proof is a simple criterion for determining if a sandpile is explosive; this strengthens a result of Fey, Levine and Peres (J. Stat. Phys. (2010) 138 143-159).
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作者：Bresler, Guy; Nagaraj, Dheeraj; Nichani, Eshaan
作者单位：Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Princeton University
摘要：In this paper, we consider the problem of sampling from the low temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an exponentially large mixing time due to metastable states. We instead consider metastable mixing, a notion of approximate mixing relative to the stationary distribution, for which it turns out to suffice to mix only within a collection of metastable states. We s...
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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：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：Cass, Thomas; Lyons, Terry; Xu, Xingcheng
作者单位：Imperial College London; University of Oxford
摘要：Suppose that gamma and sigma are two continuous bounded variation paths, which take values in a finite-dimensional inner product space V. The recent papers (J. Mach. Learn. Res. 20 (2019) 1-45) and (SIAM J. Math. Data Sci. 3 (2021) 873-899), respectively, introduced the truncated and the untruncated signature kernel of gamma and sigma, and showed how these concepts can be used in classification and prediction tasks involving multivariate time series. In this paper, we introduce signature kerne...
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作者：Feldheim, Ohad Noy; Gurel-Gurevich, Ori; Li, Jiange
作者单位：Hebrew University of Jerusalem; Harbin Institute of Technology
摘要：In the two-thinning balls-and-bins model, an overseer is provided with uniform random allocation of m balls into n bins in an on-line fashion. The overseer may reject the allocation of each ball, in which case it is placed into a new bin, drawn independently, uniformly at random. The purpose of the overseer is to reduce the maximum load, that is, the difference between the maximum number of balls in a single bin and the average number of balls among all bins. We provide tight estimates for thr...
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作者：Birkner, Matthias; Dahmer, Iulia; Diehl, Christina S.; Kersting, Goetz
作者单位：Johannes Gutenberg University of Mainz; Goethe University Frankfurt
摘要：We consider Beta(2 - alpha, alpha)-coalescents with parameter range 1 < alpha < 2 starting from n leaves. The length l(r)((n)) of order r in the n-Beta(2 - alpha, alpha)-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with r leaves. We show that for any s is an element of N the vector of suitably centered and rescaled lengths of orders 1 <= r <= s converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.
