-
作者：Bobrowski, Omer; Kahle, Matthew; Skraba, Primoz
作者单位：Duke University; University System of Ohio; Ohio State University; Slovenian Academy of Sciences & Arts (SASA); Jozef Stefan Institute; University of Primorska; Technion Israel Institute of Technology
摘要：We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-k in persistent homology, for a either the Cech or the Vietoris-Rips filtration built on a uniform Poisson process of intensity n in the unit cube [0, 1](d). This is a natural way of measuring the largest k-dimensional hole in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally ...
-
作者：Juengel, Ansgar; Yue, Wen
作者单位：Technische Universitat Wien
摘要：Discrete convex Sobolev inequalities and Beckner inequalities are derived for time-continuous Markov chains on finite state spaces. Beckner inequalities interpolate between the modified logarithmic Sobolev inequality and the Poincare inequality. Their proof is based on the Bakry-Emery approach and on discrete Bochner-type inequalities established by Caputo, Dai Pra and Posta and recently extended by Fathi and Maas for logarithmic entropies. The abstract result for convex entropies is applied t...
-
作者：Clement, Dombry; Landy, Rabehasaina
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur
摘要：A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex analysis and is expressed in terms of the residues of the function 1/(1 - g). Under the assumption that g can be extended into a meromorphic function on the complex plane and some technical conditions, we obtain even an exact expansion of the renewal function. An...
-
作者：Chen, Guan-Yu; Hsu, Jui-Ming; Sheu, Yuan-Chung
作者单位：National Yang Ming Chiao Tung University
摘要：In this article, we considers reversible Markov chains of which L-2-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [J. Funct. Anal. 258 (2010) 2246-2315], while we provide here a completely different pathway to analyze the L-2-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between...
-
作者：Jarai, Antal A.
作者单位：University of Bath
摘要：We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 <= t <= n, a uniformly random vertex v is an element of V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0,...,0) is reached. Our main result is that there is a phase transition: as n -> infinity, the expected r...
-
作者：Cai, Jiatu; Rosenbaum, Mathieu; Tankov, Peter
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. A comprehensive list of examples with explicit expression...
-
作者：Lalley, Steven; Su, Wei
作者单位：University of Chicago
摘要：We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the cutoff phenomenon in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any epsilon > 0, when the number n of vertices is large then (a) at times t < (C - epsilon) log n the fraction of ...
-
作者：Leobacher, Gunther; Szolgyenyi, Michaela
作者单位：University of Graz; Vienna University of Economics & Business; Johannes Kepler University Linz; Vienna University of Economics & Business
摘要：In this paper, we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method that converges with strong order 1/2. Our result is the first one that shows existence and uniqueness as well as strong convergence for such a general class of SDEs. The proof is based on a transformation technique that removes the disconti...
-
作者：Dommers, S.; Den Hollander, F.; Jovanovski, O.; Nardi, F. R.
作者单位：Ruhr University Bochum; Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：In this paper, we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the configuration model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferro-magnetic pair potential. We start from th...
-
作者：Bou-Rabee, Nawaf; Maria Sanz-Serna, Jesus
作者单位：Rutgers University System; Rutgers University Camden; Universidad Carlos III de Madrid
摘要：Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory way. In this article, we present and analyze a randomized HMC method (RHMC), in which these durations are i.i.d. exponential random variables whose mean is a free parameter. We focus on the small time step size limit, where the algorithm is rejection-free an...
