Gurel Gurevich , O (Hebrew University of Jerusalem)
Wednesday 22 April 2015, 15:30-16:30

Gurel Gurevich , O (Hebrew University of Jerusalem) Wednesday 22 April 2015, 15:30-16:30

Recurrence of planar graph limits

A new frontier has emerged at the interface between probability, geometry, and analysis, with a central target to produce a coherent theory of the geometry of random structures. The principal question is the following: within a given structure, what is the interplay between randomness and geometry? More precisely, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations "average out" at sufficiently large scales? Can the global geometry be described by taking a suitable scaling limit that allows for concrete computations?

Spectacular progress has been made over the last ten years in this domain. The goal of the programme is to gather experts from probability, geometry, analysis and other connected areas, in order to study aspects of this question in some paradigmatic situations. Topics of particular relevance include the Gaussian Free Field, random planar maps and Liouville quantum gravity, in connection with conformally invariant scaling limits; spin glass models and branching random walks; percolation and random graphs; and random walks on graphs and groups in the case where the geometry is determined by some algebraic ambient structure.

A new frontier has emerged at the interface between probability, geometry, and analysis, with a central target to produce a coherent theory of the geometry of random structures. The principal question is the following: within a given structure, what is the interplay between randomness and geometry? More precisely, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations "average out" at sufficiently large scales? Can the global geometry be described by taking a suitable scaling limit that allows for concrete computations? Spectacular progress has been made over the last ten years in this domain. The goal of the programme is to gather experts from probability, geometry, analysis and other connected areas, in order to study aspects of this question in some paradigmatic situations. Topics of particular relevance include the Gaussian Free Field, random planar maps and Liouville quantum gravity, in connection with conformally invariant scaling limits; spin glass models and branching random walks; percolation and random graphs; and random walks on graphs and groups in the case where the geometry is determined by some algebraic ambient structure.

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Recurrence of planar graph limits

Recurrence of planar graph limits

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