-
作者：Benaim, Michel; Gauthier, Carl-Erik
作者单位：University of Neuchatel
摘要：Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space M x R-n; which is obtained via a natural change of variable from a self-repelling diffusion taking the form dX(t) = sigma dB(t)(X-t) - integral(t)(0) del V-Xs (X-t)dsdt, X-0 = x where {B-t} is a Brownian vector field on M, sigma > 0 and V-x(y) = V(x, y) is a diagonal Mercer kernel. We prove that the ind...
-
作者：Bhamidi, Shankar; Sen, Sanchayan; Wang, Xuan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：The last few years have witnessed tremendous interest in understanding the structure as well as the behavior of dynamics for inhomogeneous random graph models to gain insight into real-world systems. In this study we analyze the maximal components at criticality of one famous class of such models, the rank-one inhomogeneous random graph model (Norros and Reittu, Adv Appl Probab 38(1):59-75, 2006; Bollobas et al., Random Struct Algorithms 31(1):3-122, 2007, Section 16.4). Viewing these componen...
-
作者：Ramirez, Jose A.; Rider, Brian
作者单位：Universidad Costa Rica; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：We characterize the limiting smallest eigenvalue distributions (or hard edge laws) for sample covariance type matrices drawn from a spiked population. In the case of a single spike, the results are valid in the context of the general ensembles. For multiple spikes, the necessary construction restricts matters to real, complex or quaternion ( or 4) ensembles. The limit laws are described in terms of random integral operators, and partial differential equations satisfied by the corresponding dis...
-
作者：[Anonymous]
-
作者：Hoffman, Christopher; Rizzolo, Douglas; Slivken, Erik
作者单位：University of Washington; University of Washington Seattle; University of Delaware; University of California System; University of California Davis
摘要：Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study fixed points of both 123- and 231-avoiding permutations. We find an exact description for a scaling limit of the empirical distribution of fixed points in terms of Brownian excursion. This builds on the connections between pattern-avoiding permutations and Brownian excursion developed in Hoff...
-
作者：Hutchcroft, Tom; Nachmias, Asaf
作者单位：University of British Columbia; Tel Aviv University
摘要：We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini et al. (Ann Probab 29(1):1-65, 2001). We also answer positively two additional questions of Benjamini et al. (Ann Probab 29(1):1-65, 2001) under the assu...
-
作者：Amini, Omid; Devroye, Luc; Griffiths, Simon; Olver, Neil
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); McGill University; University of Oxford; Vrije Universiteit Amsterdam; Centrum Wiskunde & Informatica (CWI)
摘要：Let T be an infinite rooted tree with weights assigned to its edges. Denote by the minimum weight of a path from the root to a node of the nth generation. We consider the possible behaviour of with focus on the two following cases: we say T is explosive if lim(n ->infinity) m(n)(T) < infinity, and say that T exhibits linear growth if lim inf(n -> 8) m(n)(T)/n > 0. We consider a class of infinite randomly weighted trees related to the Poisson-weighted infinite tree, and determine precisely whic...
