Séminaire du LPTMS: Jerome K. Percus


11:00 - 12:00

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

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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)

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