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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 37A35 4 results

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Phase transitions on one-dimensional symbolic systems - Kucherenko, Tamara (Author of the conference) | CIRM H

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We discuss various mechanisms for generating phase transitions on compact symbolic systems in one dimension. We present several results, classical and recent, concerning the number and frequency of phase transitions, as well as the existence of freezing phase transitions. In the latter case we focus on the type of potentials which would trigger a freezing phase transition and the support of the resulting ground state.

37D35 ; 37B10 ; 37A35

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Growth and co-growth in negatively curved groups: a dynamical point of view (part 1) - Coulon, Rémi (Author of the conference) | CIRM H

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This mini-course is an introduction to growth problems in negatively curved groups with an emphasis on techniques borrowed from dynamical systems, in particular the study of geodesic flow on hyperbolic manifolds.

20F67 ; 20F65 ; 37A35 ; 37A15 ; 37D40

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On some operator-theoretic aspects of ergodic theory - Haase, Markus (Author of the conference) | CIRM H

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I will describe the main features and methods of a strictly operator-theoretic/functional-analytic perspective on structural ergodic theory in the spirit and in continuation of a recent book project (with T.Eisner, B.Farkas and R.Nagel). The approach is illustrated by a review of some classical results by Abramov on systems with quasi-discrete spectrum and by Veech on compact group extensions (joint work with N.Moriakov).

37A30 ; 37A35 ; 37A55 ; 37B05 ; 47A35 ; 47Nxx ; 22CXX

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Typicality and entropy of processes on infinite trees - Backhausz, Agnes (Author of the conference) | CIRM H

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We consider a special family of invariant random processes on the infinite d-regular tree, which is closely related to random d-regular graphs, and helps understanding the structure of these finite objects. By using different notions of entropy and finding inequalities between these quantities, we present a sufficient condition for a process to be typical, that is, to be the weak local limit of functions on the vertices of a randomly chosen d-regular graph (with fixed d, and the number of vertices tending to infinity). Our results are based on invariant couplings of the process with another copy of itself. The arguments can also be extended to processes on unimodular Galton-Watson trees. In the talk we present the notion of typicality, the entropy inequalities that we use and the sufficient conditions mentioned above. Joint work with Charles Bordenave and Balázs Szegedy.[-]
We consider a special family of invariant random processes on the infinite d-regular tree, which is closely related to random d-regular graphs, and helps understanding the structure of these finite objects. By using different notions of entropy and finding inequalities between these quantities, we present a sufficient condition for a process to be typical, that is, to be the weak local limit of functions on the vertices of a randomly chosen ...[+]

05C80 ; 37A35 ; 28D20

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