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Showing 2012 · math.PRShow all

15 papers · 2 filters

math.PR2012★ 37 cited

Non-backtracking random walk

Robert Fitzner, Remco van der Hofstad

We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the Zd-lattice and on tori. We evaluate the eigensystem of the m X m-dimensional transition matrix…

math.PR2012★ 17 cited

Short paths for first passage percolation on the complete graph

Maren Eckhoff, Jesse Goodman, Remco van der Hofstad +1

We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number…

math.PR2012★ 1 cited

Queues and risk models with simultaneous arrivals

E. S. Badila, O. J. Boxma, J. A. C. Resing +1

We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel…

math.PR2012★ 2 cited

Logarithmic asymptotics for multidimensional extremes under non-linear scalings

Kamil Marcin Kosinski, Michel Mandjes

Let be a sequence of random vectors in , . This paper considers the logarithmic asymptotics of the extremes o…

math.PR2012★ 2 cited

Decomposition results for stochastic storage processes and queues with alternating Lévy inputs

Onno Boxma, Offer Kella

In this paper we generalize known workload decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases…

math.PR2012★ 1 cited

Mixing Properties of CSMA Networks on Partite Graphs

Alessandro Zocca, Sem C. Borst, Johan S. H. van Leeuwaarden

We consider a stylized stochastic model for a wireless CSMA network. Experimental results in prior studies indicate that the model provides remarkably accurate throughput estimates…

math.PR2012

Random walk on the high-dimensional IIC

Markus Heydenreich, Remco van der Hofstad, Tim Hulshof

We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by…

math.PR2012★ 12 cited

Kawasaki dynamics with two types of particles: critical droplets

Frank den Hollander, Francesca Romana Nardi, Alessio Troiani

This is the third in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature i…

math.PR2012

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

Amaury Lambert, Florian Simatos

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with non-zero Lévy measure. In this paper we…

math.PR2012★ 4 cited

The abelian sandpile model on a random binary tree

Frank Redig, Ellen Saada, Wioletta Ruszel

We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a sm…

math.PR2012★ 95 cited

Degree-degree correlations in random graphs with heavy-tailed degrees

Nelly Litvak, Remco van der Hofstad

Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies}…

math.PR2012★ 7 cited

A stochastic network with mobile users in heavy traffic

Sem Borst, Florian Simatos

We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial…

math.PR2012

The weak convergence of regenerative processes using some excursion path decompositions

Amaury Lambert, Florian Simatos

We consider regenerative processes with values in some Polish space. We define their ε-big excursions as excursions e such that f(e)>ε, where f is some given functional on the spac…

math.PR2012★ 17 cited

Levy multiplicative chaos and star scale invariant random measures

Rémi Rhodes, Julien Sohier, Vincent Vargas

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize…

math.PR2012★ 14 cited

First Passage Percolation on Inhomogeneous Random Graphs

István Kolossváry, Júlia Komjáthy

We investigate first passage percolation on inhomogeneous random graphs. The random graph model G(n,kappa) we study is the model introduced by Bollobás, Janson and Riordan, where e…