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Seminários do IMPA

Geometria Diferencial

 Título Random walk on groups: Martin Boundary and Floyd boundary Expositor Victor Gerassimov Universidade Federal de Minas Gerais Data Terça-feira, 6 de novembro de 2018, 14:00 Local Sala 333 Resumo

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.