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Monthly Archives: January 2014
Notes of Gady Kozma’s lecture
Harmonic functions of minimal growth With Amir, Benjamini, DuminilCopin, Meyerovich, Yadin. 1. Motivation Gromov’s polynomial growth theorem. Kleiner’s new proof that uses Lipschitz harmonic functions. Any group has non trivial Lipschitz harmonic functions. Polynomial growth implies that they form a … Continue reading
Notes of Bertrand Deroin’s lecture
Random walks on leftorderable groups I view random walks as a tool to study leftorderable groups. 1. Leftorderable groups This means a group with a leftinvariant order. Torsion in an obstruction. Not easy to find firther obstructions, and indeed, many … Continue reading
Notes of Itai Benjamini’s 2014 lecture
Invariant random structures 1. First passage percolation Multiply length of edges of the 2grid by 1 or 10 with equal probabilities. Known : there is an asymptotic shape. What is it ? UIPT : the limit is not deterministic. Stationary … Continue reading
Notes of Bartosz Trojan’s lecture
Heat kernel on affine buildings Consider finite support probability distributions on an affinebuiding which are spherical : depends only on distance. Plays the role of heat kernel on symmetric spaces. For such a kernel, one has rather sharp asymptotic estimates … Continue reading
Notes of Ryokichi Tanaka’s lecture
Discrete random walks on SOL Joint with J. Brieussel. 1. Case of Theorem 1 (Furstenberg (1963)) Let be an absolutely continuous probability measure on . Then converges to the circle, with asymptotic distribution equal to harmonic measure. This is not … Continue reading
Notes of Yuval Peres’ 2014 lecture
The Poisson boundary of lamplighter groups Joint with R. Lyons. 1. Entropy The whole subject started with Kesten in 1949 and Furstenberg in early 50’s. Entropy on the boundary. In 1970, Avez proposed to define entropy directly on the group. … Continue reading
Notes of Antonio Lerario’s lecture
Loop spaces in subRiemannian manifolds with Agrachev and Gentile. Let be a subRiemannian manifold. How complicated is the space of admissible curves joning and with energy ? By complicated, I mean topologically complicated, as measured by the sum of Betti … Continue reading