Séminaire du LPTMS: Jerome K. Percus

Quand

10/11/2015    
11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

Type d’évènement

Chargement de la carte…

Random walks that generate their own environment

J.K. Percus, Courant Inst and Physics Dept, New York University

The term « random walk in a random environment » covers many phenomena in applied science. Most frequently, it refers to two independent random processes. We will look at the opposite extreme, in which the previous state of a – typically next neighbor walk on a lattice -changes the parameters of the current site. A primitive example that can be interpreted in this way is that of the statistics of the maximum of a walk on the half line, where we would expect a substantially increased mean and a substantially decreased variance over that of the underlying walk. How extreme are these? A more structured example, of relevance to synaptic strengthening, is that of a reinforced random walk, in which the first visit to a given site strengthens the « attraction » of that site for future visits, and this is quite simple in the Brownian motion limit. Still more nuanced is the situation in which the « attraction » depends upon the number of previous visits.

(in collaboration with O.E. Percus)

Retour en haut