From September 2011, the RSS seminars will be integrated in the new STO(chastics) Seminar Series.
Please follow the link for further details.

In joint work with Tom Salisbury, we study random walks in i.i.d. random environments in dimensions 2 and higher. In our environments, at any given site some steps may not be available to the random walker (i.e. we don't assume ellipticity). Among our main results are 0-1 laws for directional transience (extending results already known under the assumption of ellipticity) and a simple monotonicity result for 2-valued environments (at each site the environment takes one of two values).

Carlo Lancia (Universita Tor Vergata, Rome)

We present within the context of finite Markov chains a theorem relating the cutoff-time to suitably chosen random times. We have in mind the generalization of the link between hitting times and cutoff to systems with uniform stationary measure. Such link has been already proved in literature, though only for families of chains whose stationary measure is concentrated in a small region of the state space.
We employ this result to prove cutoff for the random walk on the hypercube and a partially-diffusive random walk.

Ivan Corwin (Courant Institute at NYU, USA)

The Gaussian central limit theorem says that for a wide class of stochastic systems, the bell curve (Gaussian distribution) describes the statistics for random fluctuations of important observables. In this talk I will look beyond this class of systems to a collection of probabilistic models which include random growth models, polymers, particle systems, matrices and stochastic PDEs, as well as certain asymptotic problems in combinatorics and representation theory. I will explain in what ways these different examples all fall into a single new universality class with a much richer mathematical structure than that of the Gaussian.

The parabolic Anderson model: The asymptotics of the statistical moments and Lifshitz tails revisited

Abstract

In this talk we give a brief introduction to the theory of stochastic flows and state some actual problems related to this field. In particular, stochastic integration with respect to a flow with singularities will be discussed, a Girsanov-type theorem and a large-deviations principle for flows of Brownian particles will be presented.

Lace expansion for dummies

After the first contact to the lace expansion most people are terrified by the involved analysis and the sheer amount of necessary notation. For this reason I want to give a simple and short (30 minutes) introduction of the lace expansion argumentation. We will see the how to prove a fundamental result about the relation between the simple random walk and the self-avoiding walks, This result can be used prove that for dimension bigger than 4 the self-avoiding walk on the Zd-lattice, when properly scaled, converge to Brownian  Motion.

Random walks in a random environment on the positive integers

The mixing measure of a recurrent random walk in an irreducible random environment on a locally finite connected graph is unique. For example, the linearly edge-reinforced random walk on such a graph is a mixture of irreducible Markov chains, as was proved by Merkl and Rolles. However, for some locally finite connected graphs it is not known if this stochastic process is recurrent. In many situations transience of the edge-reinforced random walk can be observed. We show that on the positive integers the mixing measure for a random walk in a random environment is unique irrespective of the recurrence of the random walk. This is the joint work with Silke W.W. Rolles.

B. Scoppola, (Università degli Studi di Roma Tor Vergata)

Queueing systems with pre-scheduled random arrivals

We study a queueing system with deterministic service times and with arrivals defined in terms of a random translation of the set of integers. We show that, althought the arrival process of the system is very similar to a Poisson process, the congestion is very different. We will present an approximation scheme to compute the distribution of the length of the queue. The model is motivated by the description of the air traffic. We will present a comparison between our results and real data.

Last updated 14-10-11
Maintained by PK

    P.O. Box 513, 5600 MB  Eindhoven, The Netherlands
tel. +31 40 2478100  fax +31 40 2478190  
  e-mail: info@eurandom.tue.nl