Probability Theory and Related Fields

最新文章

• Convergence of the reach for a sequence of Gaussian-embedded manifolds AI翻译
  作者：Adler, Robert J.; Krishnan, Sunder Ram; Taylor, Jonathan E.; Weinberger, Shmuel
  作者单位：Technion Israel Institute of Technology; Stanford University; University of Chicago
  摘要：Motivated by questions of manifold learning, we study a sequence of random manifolds, generated by embedding a fixed, compact manifold M into Euclidean spheres of increasing dimension via a sequence of Gaussian mappings. One of the fundamental smoothness parameters of manifold learning theorems is the reach, or critical radius, of M. Roughly speaking, the reach is a measure of a manifold's departure from convexity, which incorporates both local curvature and global topology. This paper develop...
• Small-time fluctuations for sub-Riemannian diffusion loops AI翻译
  作者：Habermann, Karen
  作者单位：University of Cambridge
  摘要：We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the span of the sub-Riemannian structure. In the case where the endpoints agree and the generator of the diffusion process is non-elliptic at that point, the deterministic Malliavin covariance matrix is always degenerate. We identify, after a suitable rescaling, ...
• Escape regimes of biased random walks on Galton-Watson trees AI翻译
  作者：Bowditch, Adam
  作者单位：University of Warwick
  摘要：We study biased random walk on subcritical and supercritical Galton-Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which, in this case, always yield sub-ballisticity. This is contrary to the walk on the supercritical tree which always has some ballistic phase.
• Recurrence and density decay for diffusion-limited annihilating systems AI翻译
  作者：Cabezas, M.; Rolla, L. T.; Sidoravicius, V.
  作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Pontificia Universidad Catolica de Chile; University of Buenos Aires; New York University; NYU Shanghai; New York University
  摘要：We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D-A > 0 and D-B >= 0, and the interaction is given by mutual annihilation A + B -> empty set. The initial condition is i.i.d. with finite first moment. We show that this system is site-recurrent, that is, each site is visited infinitely many times. We also generalize a lower bound on the density decay of Bramson and Lebowitz by considering a construction t...
• On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators AI翻译
  作者：El Karoui, Noureddine
  作者单位：University of California System; University of California Berkeley
  摘要：We study ridge-regularized generalized robust regression estimators, i.e. in the situation where p/n tends to a finite non-zero limit. Our study here focuses on the situation where the errors 's are heavy-tailed and 's have an elliptical-like distribution. Our assumptions are quite general and we do not require homoskedasticity of 's for instance. We obtain a characterization of the limit of , as well as several other results, including central limit theorems for the entries of (beta) over cap.
• Dyson Ferrari-Spohn diffusions and ordered walks under area tilts AI翻译
  作者：Ioffe, Dmitry; Velenik, Yvan; Wachtel, Vitali
  作者单位：Technion Israel Institute of Technology; University of Geneva; University of Augsburg
  摘要：We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of -dimensional discrete-height random surfaces in statistical mechanics. We prove that, under rather general assumptions on the step distribution and on the self-potential, such walks converge, under appropriate rescaling, to non-intersecting Ferrari-Spohn diffusions associated with limiting S...
• Limits of the boundary of random planar maps AI翻译
  作者：Richier, Loic
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter it has a component homeomorphic to the half-plane. As an application, we identify the limits of loops conditioned to be large in the rigid loop model on quadrangulations, proving thereby a conjecture of Curien and Kortchemski.
• Scaling limits of random Polya trees AI翻译
  作者：Panagiotou, Konstantinos; Stufler, Benedikt
  作者单位：University of Munich; Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：Polya trees are rooted trees considered up to symmetry. We establish the convergence of large uniform random Polya trees with arbitrary degree restrictions to Aldous' Continuum Random Tree with respect to the Gromov-Hausdorff metric. Our proof is short and elementary, and it is based on a novel decomposition: it shows that the global shape of a random Polya tree is essentially dictated by a large Galton-Watson tree that it contains. We also derive sub-Gaussian tail bounds for both the height a...
• Concentration inequalities for matrix martingales in continuous time AI翻译
  作者：Bacry, Emmanuel; Gaiffas, Stephane; Muzy, Jean-Francois
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS)
  摘要：This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermartingale property of the trace exponential proved within the framework of stochastic calculus. We provide also several examples that illustrate the fact that our results allow us to...
• The multiplicative coalescent, inhomogeneous continuum random trees, and new universality classes for critical random graphs AI翻译
  作者：Bhamidi, Shankar; van der Hofstad, Remco; Sen, Sanchayan
  作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; McGill University
  摘要：One major open conjecture in the area of critical random graphs, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys Rev Lett 91(16):168701, 2003; Wu et al. in Phys Rev Lett 96(14):148702, 2006; Braunstein et al. Int J Bifurc Chaos 17(07):2215-2255, 2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006) is as follows: for a wide array of random graph models with degree exponent , distances between typical p...