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| Speaker |
Martin Zerner, University of Tuebingen |
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| Title |
On random ranchers and cookie monsters: some self-interacting
random walks with bias. |
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| Abstract |
We consider two models of self-interacting random walks:
1. Excited Random Walks:
We put two cookies on each integer and start a random walker at 0.
Whenever there is at least one cookie at the walker's present location,
the walker eats one of these cookies and then jumps to the right with
probability p and to the left with probability 1-p, where p is a fixed
parameter greater than 1/2. At sites without any cookies left over the
walker jumps with probability 1/2 to the right and 1/2 to the left.
We consider recurrence, transience and the speed of this and similar walks.
Such models have also been investigated e.g. by Benjamini, Wilson,
Kozma and Volkov.
2. Random Rancher:
We consider a model due to Angel, Benjamini and Virag,
in which a random walker in the plane takes steps of length one but
avoids the convex hull of its past positions. We show that this walk
has positive lim inf speed |
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| Speaker |
Max von Renesse, TU Berlin, CIMS |
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| Title |
A preliminary talk for the geometers introducing the necessary probability techniques. |
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| Abstract | This will be a preliminary talk for the speaker's 4pm talk |
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| Speaker |
Max von Renesse, TU Berlin, CIMS |
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| Title |
Mass Transportation and Synthetic Ricci Curvature Bounds |
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| Abstract | The problem of optimal mass transportation has appeared first in
the 18th century in economic models. In recent years the theory
has undergone a remarkable development with applications in PDE,
probability and geometry. The talk will give a short review of
some basic concepts involved. The focus of the second part will be
geometric. Mass transportation is used for the defintion and
analysis of generalized lower Ricci curvature bounds for metric
measure spaces with no or almost no regularity.
(This talk is given in Differential Geometry and Lie Theory seminar.
The talk is at 4pm, but in room 4419 not our usual 5417.) |
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| Speaker |
Gady Kozma,, IAS |
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| Title |
Isoperimetric inequalities in probability |
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| Abstract |
This talk will survey connection between isoperimetric
inequalities on infinite graphs and random walk and percolation on
these graphs.
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| Speaker |
Anotonia Földes, CUNY, |
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| Title |
Joint asymptotic behavior of local and occupation times |
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| Abstract |
Considering a simple symmetric random
walk in dimension 3 or higher, we study the almost sure joint
asymptotic behavior of two objects: first the local times of a
pair of neighboring points, then the local time of a point and the
occupation time of the surface of the unit ball around it.
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| Speaker |
Natella O'Bryant, College of Staten Island, CUNY |
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| Title |
Ballistic points of finite-mode Kolmogorov flows |
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| Abstract |
This talk is of purely mathematical nature, but some
connections to problems dealing with turbulence of incompressible
fluids will be drawn. We consider planar flows driven by velocity
fields with prescribed spectrum of Kolmogorov's type. Knowing that a
finite-mode approximation of such a flow expands diameters of certain
sets linearly in time, we show that a point moving with linear speed
is guaranteed to be found almost surely. A similar result is known to
hold for isotropic Brownian flows with strictly positive Lyapunov
exponent, and also for more general martingale flows, and has been
conjectured for the 'full' Kolmogorov flow as well.
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|
| Speaker |
Greg Markowsky, CUNY |
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| Title |
The derivative of intersection local time in two dimensions |
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