The Annals of Applied Probability

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• CONTINUOUS-TIME WEAKLY SELF-AVOIDING WALK ON Z HAS STRICTLY MONOTONE ESCAPE SPEED AI翻译
  作者：Liu, Yucheng
  作者单位：University of British Columbia
  摘要：Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On Z, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing...
• CONVERGENCE OF ADAPTED EMPIRICAL MEASURES ON Rd AI翻译
  作者：Acciaio, Beatrice; Hou, Songyan
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：nite discrete-time. We show that the adapted empirical measure introduced in in compact spaces can be defined analogously on Rd, and that it converges almost surely to the underlying measure under the adapted Wasserstein distance. Moreover, we quantitatively analyze the convergence of the adapted Wasserstein distance between those two measures. We establish convergence rates of the expected error as well as the deviation error under different moment conditions. Under suitable integrability and...
• LOCALIZATION OF A ONE-DIMENSIONAL SIMPLE RANDOM WALK AMONG POWER-LAW RENEWAL OBSTACLES AI翻译
  作者：Poisat, Julien; Simenhaus, Francois
  作者单位：Universite PSL; Universite Paris-Dauphine
  摘要：We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the large-time asymptotics of the quenched survival probability. In the present work we continue our study by describing the behaviour of the random walk conditioned to survive. We prove that with large probability, the walk quickly reaches a unique time-dependent optima...
• STOCHASTIC VOLTERRA EQUATIONS FOR THE LOCAL TIMES OFSPECTRALLY POSITIVE STABLE PROCESSES AI翻译
  作者：Xu, Wei
  作者单位：Beijing Institute of Technology
  摘要：This paper is concerned with the evolution dynamics of local times ofa spectrally positive stable process in the spatial direction. The main resultsstate that conditioned on the finiteness of the first time at which the local timeat zero exceeds a given value, the local times at positive half line are equal indistribution to the unique solution of a stochastic Volterra equation driven bya Poisson random measure whose intensity coincides with the L & eacute;vy measure.This helps us to provide n...
• FINITE SAMPLE COMPLEXITY OF SEQUENTIAL MONTE CARLO ESTIMATORS ON MULTIMODAL TARGET DISTRIBUTIONS AI翻译
  作者：Mathews, Joseph; Schmidler, Scott C.
  作者单位：Duke University
  摘要：We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the Markov kernel is slow; in such cases our approach establishes the benefits of SMC over the corresponding Markov chain Monte Carlo (MCMC) estimator. The lack of global mixing is addressed by sequentially controlling the bias introduced by SMC r...
• FROM FINITE POPULATION OPTIMAL STOPPING TO MEAN FIELD OPTIMAL STOPPING AI翻译
  作者：Talbi, Mehdi; Touzi, Nizar; Zhang, Jianfeng
  作者单位：Universite Paris Cite; New York University; New York University Tandon School of Engineering; University of Southern California
  摘要：This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterization of the mean field optimal stopping problem of our previous papers ( SIAM J. Control Optim. 61 (2023) 1712-1736, 2140-2164), we prove the convergence of the value functions by adapting the Barles-Souganidis ( Asymptot. Anal. 4 (1991) 271-283) monotone scheme method to our context. We next characterize the optimal st...
• THE LANDSCAPE OF THE PLANTED CLIQUE PROBLEM: DENSE SUBGRAPHS AND THE OVERLAP GAP PROPERTY AI翻译
  作者：Amarnik, David; Adik, Ilias
  作者单位：Massachusetts Institute of Technology (MIT); New York University
  摘要：We study the computational-statistical gap of the planted clique problem, where a clique of size k is planted in an Erdos-Renyi graph G(n, 1/2). The goal is to recover the planted clique vertices by observing the graph. It is known that the clique can be recovered as long as k >= (2 + epsilon) log n for any epsilon > 0, but no polynomial-time algorithm is known for this task unless k = Omega (root n). Following a statistical-physics inspired point of view, as a way to understand the nature of ...
• PAIRWISE SEQUENCE ALIGNMENT AT ARBITRARILY LARGE EVOLUTIONARY DISTANCE AI翻译
  作者：Legried, Brandon; Roch, Sebastien
  作者单位：University System of Georgia; Georgia Institute of Technology; University of Wisconsin System; University of Wisconsin Madison
  摘要：Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many biological applications, it has played a key role in elucidating the statistical performance of phylogeny estimation methods. Here we establish a formal connection to another important bioinformatics problem, multiple sequence alignment, where one attempts ...
• EXTREMAL STATISTICS OF QUADRATIC FORMS OF GOE/GUE EIGENVECTORS AI翻译
  作者：Erdos, Laszlo; McKenna, Benjamin
  作者单位：Institute of Science & Technology - Austria
  摘要：We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N x N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than root N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, wh...
• DISCRETE STICKY COUPLINGS OF FUNCTIONAL AUTOREGRESSIVE PROCESSES AI翻译
  作者：Durmus, Alain; Eberle, Andreas; Enfroy, Aurelien; Guillin, Arnaud; Monmarche, Pierre
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; University of Bonn; Universite Paris Saclay; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
  摘要：In this paper, we provide bounds in Wasserstein and total variation distances between the distributions of the successive iterates of two functional autoregressive processes with isotropic Gaussian noise of the form Yk+1 = T gamma (Yk)+ gamma sigma 2Zk+1 and Yk+1 = T gamma ( Yk)+ gamma sigma 2 Zk+1. More precisely, we give nonasymptotic bounds on rho(L(Yk),L( Yk)), where rho is an appropriate weighted Wasserstein distance or a V-distance, uniformly in the parameter gamma , and on rho (pi gamma...