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Showing 2011 · math.PRShow all

16 papers · 2 filters

math.PR2011

Occupation densities in solving exit problems for Markov additive processes and their reflections

Jevgenijs Ivanovs, Zbigniew Palmowski

This paper solves exit problems for spectrally negative Markov additive processes and their reflections. A so-called scale matrix, which is a generalization of the scale function o…

math.PR2011★ 3 cited

A Lévy input fluid queue with input and workload regulation

Zbigniew Palmowski, Maria Vlasiou, Bert Zwart

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers according to a spectrally positive Lévy process $Y…

math.PR2011

The survival probability and r-point functions in high dimensions

Remco van der Hofstad, Mark Holmes

In this paper we investigate the survival probability, θ_n, in high-dimensional statistical physical models, where θ_n denotes the probability that the model survives up to time n.…

math.PR2011★ 4 cited

Uniform mixing time for Random Walk on Lamplighter Graphs

Júlia Komjáthy, Jason Miller, Yuval Peres

Suppose that $\CG$ is a finite, connected graph and is a lazy random walk on $\CG$. The lamplighter chain associated with is the random walk on the wreath prod…

math.PR2011★ 2 cited

Cycle structure of percolation on high-dimensional tori

Remco van der Hofstad, Artem Sapozhnikov

In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been establishe…

math.PR2011★ 4 cited

High-dimensional Gaussian fields with isotropic increments seen through spin glasses

Anton Klimovsky

We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational represen…

math.PR2011★ 1 cited

High-dimensional incipient infinite clusters revisited

Markus Heydenreich, Remco van der Hofstad, Tim Hulshof

The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we constru…

math.PR2011★ 11 cited

Antiferromagnetic Potts model on the Erdos-Renyi random graph

Pierluigi Contucci, Sander Dommers, Cristian Giardina' +1

We study the antiferromagnetic Potts model on the Poissonian Erdös-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, toge…

math.PR2011★ 29 cited

Queue lengths and workloads in polling systems

Onno Boxma, Offer Kella, Kamil Marcin Kosinski

We consider a polling system: a queueing system of queues with Poisson arrivals visited in a cyclic order (with or without switchover times) by a single serv…

math.PR2011★ 19 cited

Kawasaki dynamics with two types of particles: stable/metastable configurations and communication heights

Frank den Hollander, Francesca R. Nardi, Alessio Troiani

This is the second 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…

math.PR2011★ 19 cited

The branching Brownian motion seen from its tip

E. Aïdékon, J. Berestycki, É. Brunet +1

It has been conjectured since the work of Lalley and Sellke (1987) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant…

math.PR2011★ 1 cited

Random walks reaching against all odds the other side of the quarter plane

Johan S. H. van Leeuwaarden, Kilian Raschel

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state , we study the event that the walk reaches the vertical ax…

math.PR2011★ 5 cited

Gaussian queues in light and heavy traffic

Krzysztof Debicki, Kamil Marcin Kosinski, Michel Mandjes

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in…

math.PR2011

Scale-free percolation

Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra

We formulate and study a model for inhomogeneous long-range percolation on $\Zbold^d$. Each vertex $x\in\Zbold^d$ is assigned a non-negative weight , where $(W_x)_{x\in\Zbold^…

math.PR2011

Metastability for Kawasaki dynamics at low temperature with two types of particles

F. den Hollander, F. R. Nardi, A. Troiani

This is the first 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.PR2011★ 244 cited

Convergence in law of the minimum of a branching random walk

Elie Aïdékon

We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044-1079] proved the tightness of the minimum centered around its…