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Seminários do IMPA

Geometria Diferencial

Random walk on groups: Martin Boundary and Floyd boundary
Victor Gerassimov

Universidade Federal de Minas Gerais
Terça-feira, 6 de novembro de 2018, 14:00
Sala 333

In the sixties of the last century it was realized by Furstenberg and others that a sample trajectory of the random walk (or its continuous analog, the Brownian motion) in the hyperbolic space $\Bbb H^n$, $n>1$, with probability one, converges to a point at the boundary $\partial\Bbb H^n$. At about the same time it was realized that two old mathematical subjects, namely the theory of random walk and the potential theory, are equivalent. 

These two observations have spawned a vast area of research. I will give an introduction to this area. I will also say something about our contribution.

A weak ago my co-author, Leonid Potyagailo gave a talk here. He kindly provided me with the summary.
My talk will not be a continuation, just another point of view on the same subject. I will not assume that the
audience is familiar with the contents of Leonid's talk. On the other hand, I will try to minimize repetition.

My purpose is the historical and conceptual background, the relations between probabilistic and geometric properties of certain ``rather homegeneous'' and ``rather hyperbolic'' spaces, mainly the Cayley graphs of certain finitely generated groups.

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Please make note of the unusual time and place for this session.