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作者：Bloemendal, Alex; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Wisconsin System; University of Wisconsin Madison
摘要：We introduce a class of M x M sample covariance matrices Q which subsumes and generalizes several previous models. The associated population covariance matrix Sigma = EQ is assumed to differ from the identity by a matrix of bounded rank. All quantities except the rank of Sigma - I-M may depend on M in an arbitrary fashion. We investigate the principal components, i. e. the top eigenvalues and eigenvectors, of Q. We derive precise large deviation estimates on the generalized components < w, xi(...
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作者：Oliveira, Roberto Imbuzeiro
摘要：Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the lower tail of such a matrix, and prove that it is sub-Gaussian under a simple fourth moment assumption on the one-dimensional marginals of the random vectors. A similar result holds for more general sums of random positive semidefinite matrices, and our (relatively simple) proof uses a variant of the so-called PAC-Bayesian method for bounding empirical processes. Us...
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作者：Knapik, B. T.; Szabo, B. T.; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam; Budapest University of Technology & Economics; Leiden University - Excl LUMC; Leiden University; University of Amsterdam
摘要：We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic smoothness, without using knowledge about this regularity. Both method...
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We first prove that, for kappa is an element of (0, 4), a whole-plane SLE(kappa; kappa + 2) trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for kappa is an element of(0, 4), a chordal SLE kappa curve stopped at a fixed capacity time can be mapped conformally to the initial segment of a whole-plane SLE(kappa; kappa+ 2) trace. A similar but weaker result holds for radial SLE.. These results are then used to study the ergodic be...
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作者：Maillard, Pascal
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are kept and the others killed. After rescaling time by , we show that the properly recentred position of the -th particle from the right, , converges in law to an explicitly given spectrally positive L,vy process. This behaviour has been predicted to hold for a large class of models falling into the ...
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作者：Fribergh, Alexander; Kious, Daniel
作者单位：Universite de Montreal; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider elliptic random walks in i.i.d. random environments on . The main goal of this paper is to study under which ellipticity conditions local trapping occurs. Our main result is to exhibit an ellipticity criterion for ballistic behavior which extends previously known results. We also show that if the annealed expected exit time of a unit hypercube is infinite then the walk has zero asymptotic velocity.
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作者：Comets, Francis; Vu-Lan Nguyen
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Consider the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppalainen (Ann Probab, 40(1):19-73, 2012). In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. We have analogous results out of eq...
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作者：Lacker, Daniel
作者单位：Princeton University
摘要：The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may be asymmetric and based on full information. It is shown that approximate Nash equilibria in the n-player games admit certain weak limits as n tends to infinity, and every limit is a weak solution of the mean field game (MFG). Conversely, every weak MFG solu...
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作者：van de Brug, Tim; Camia, Federico; Lis, Marcin
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Chalmers University of Technology; University of Gothenburg
摘要：The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a conformally invariant Poissonian ensemble of planar loops with deep connections to conformal loop ensembles (CLEs) and the Schramm-Loewner evolution (SLE). Lawler and Trujillo Ferreras showed that, r...
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作者：Sabot, Christophe; Tarres, Pierre
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem.
