Probability Theory and Related Fields

最新文章

• The lower tail of random quadratic forms with applications to ordinary least squares AI翻译
  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...
• Bayes procedures for adaptive inference in inverse problems for the white noise model AI翻译
  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...
• Ergodicity of the tip of an SLE curve AI翻译
  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...
• Speed and fluctuations of N-particle branching Brownian motion with spatial selection AI翻译
  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 ...
• Local trapping for elliptic random walks in random environments in Zd AI翻译
  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.
• Localization in log-gamma polymers with boundaries AI翻译
  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...
• A general characterization of the mean field limit for stochastic differential games AI翻译
  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...
• Random walk loop soups and conformal loop ensembles AI翻译
  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...
• Inverting Ray-Knight identity AI翻译
  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.
• On infinitely divisible semimartingales AI翻译
  作者：Basse-O'Connor, Andreas; Rosinski, Jan
  作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
  摘要：Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see Stricker (ZWahrsch Verw Geb 64(3):303-312, 1983). We consider extensions of this result to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Th...