The seminar meets on Wednesdays at 2PM in room 1313
The seminar organizers are Dmitry Dolgopyat and Leonid Koralov.
September 30
Manfred Denker
(Penn State)
Self-organized criticality in random dynamics .
In this talk I will present an "Integrate and Fire" model from neural
science, and explain the Levina (2008) representation as a discrete-time random
dynamical system. I will explain how to derive a power law for the number of firing
neurons using branching process approximation.
October 14
Mark Freidlin (UMD)
Stochasticity of almost elastic collisions
November 11, 11 AM in room 0102
NOTE SPECIAL TIME AND PLACE!
Steve Lalley (Chicago)
Return Probabilities for Random Walks on Hyperbolic Groups
November 11
Mark Kelbert (Swansea)
Probabilistic approach to high order PDE's
November 16, 2PM in room 1313
NOTE UNUSUAL DATE!
Oren Louidor
(Courant)
Directed polymers in random environment with heavy tails
We study the model of Directed Polymers in Random Environment in
1+1
dimensions, where the environment is i.i.d. with a site distribution
having a tail that decays regularly polynomially with power -\alpha,
where \alpha \in (0,2). After proper scaling of temperature \beta^{-1},
we show strong localization of the polymer to an optimal region in the
environment where energy and entropy are best balanced. We prove that
this region has a weak limit under linear scaling and identify the
limiting distribution as an (\alpha, \beta)-indexed family of measures
on Lipschitz curves lying inside the 45^{\circ}-rotated square with
unit diagonal. In particular, this shows order of n for the transversal
fluctuations of the polymer. If (and only if) \alpha is small enough,
we find that there exists a random critical temperature above which the
effect of the environment is not macroscopically noticeable. The
results carry over to higher dimensions with minor modifications.
December 4
Elena Kosygina (CUNY)
Limit laws of excited random walks on integers
We consider excited random walks on integers with a bounded number of
i.i.d.
cookies per site without the non-negativity assumption on the drifts
induced
by the ``cookies''. We shall discuss known and new results about limit laws
of these random walks (under the averaged measure) as well as some open
questions. This is a joint work with T. Mountford, EPFL, Lausanne.
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