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Zero-one laws for binary random fields
zero-one laws binary random fields weak dependence first-order logic
2009/6/12
Zero-one laws for binary random fields.
First passage of reflected strictly stable processes
Strictly stable processes reected Levy processes overshoot distribution first passage problem
2009/6/12
First passage of reflected strictly stable processes.
The finite system scheme for state-dependent interacting
the finite system scheme state-dependent interacting
2009/6/12
The finite system scheme for state-dependent interacting multitype branching systems.
Congruence properties of depths in some random trees.
Convergence of the Tóth lattice filling curve to the Tóth-Werner plane filling curve
convergence Tóth lattice filling curve Tóth-Werner plane
2009/6/12
Convergence of the Tóth lattice filling curve to the Tóth-Werner plane filling curve.
Recurrence of simple random walk on Z2 is dynamically sensitive
recurrence simple random walk dynamically sensitive
2009/6/12
Recurrence of simple random walk on Z2 is dynamically sensitive.
Random trees and applications
random tree contour process conditioned tree Brownian motion Brownian excursion real tree coding of trees
2009/5/18
We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple ap...
Large deviations and stochastic calculus for large random matrices
large deviations random matrices non-commutative measure integration.
2009/5/18
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...
Uniqueness and non-uniqueness in percolation theory
percolation uniqueness of the infinite cluster transitive graphs amenability
2009/5/18
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on $Z^d$ and more generally on transitive graphs. For iid percolation o...
Localization and delocalization of random interfaces
random interfaces random surfaces roughening entropic repulsion pinning wetting prewetting
2009/5/18
The study of effective interface models has been quite active recently, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/d...
Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history in order to arrive at a field theoretical analog of Klauder's quantization in Hamilto...
Martingale proofs of many-server heavy-traffic limits for Markovian queues
multiple-server queues many-server heavy-traffic limits for queues diffusion approximations martingales functional central limit theorems
2009/5/18
This is an expository review paper illustrating the “martin- gale method” for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximatio...
Queueing networks constitute a large family of stochastic models, involving jobs that enter a network, compete for service, and eventually leave the network upon completion of service. Since the early...
Loop-Erased Walks Intersect Infinitely Often in Four Dimensions
Random Walks Loop-Erased Walks Intersections
2009/5/8
In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two w...
Brownian couplings, convexity, and shy-ness
Brownian motion co-adapted coupling convexity coupling Markovian coupling perversecoupling reflection coupling
2009/4/29
Benjamini, Burdzy and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component proce...