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Department of Mathematics,
University of California San Diego

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Math 196 - Undergraduate Colloquium

Jon Novak

UCSD

Polya's random walk theorem

Abstract:

This lecture will be about a remarkable law of nature discovered by George Polya. Consider a particle initially situated at a given point of the d-dimensional integer lattice. Suppose that, at each tick of the clock, the particle jumps to a neighboring lattice site, with equal probability of jumping in any direction. Polya's law states that the particle returns to its initial position with probability one in dimensions d = 1,2, but with probability strictly less than one in all higher dimensions. Thus, a drunk person wandering a city grid will always return to their starting point, but if the drunkard can fly s/he might never come back.

Organizer: Brendon Rhoades

October 18, 2016

12:00 PM

AP&M B402A

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