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Kinetically constrained spin models

Presented by: 
Cristina Toninelli Université Pierre & Marie Curie-Paris VI
Date: 
Monday 11th July 2016 - 09:45 to 10:30
Venue: 
INI Seminar Room 1
Abstract: 
We shall discuss kinetically constrained spin models (KCSM), a class ofinteracting particle systems which have been introduced in physics liter-ature to model liquid-glass and more general jamming transitions. Theevolution of KCSM follows a continuous time Markov process whoseelementary moves are birth and death of particles. The key feature isthat a move occurs only if the conguration satises a local constraint.These constraints induce the existence of clusters of blocked particles,the occurrence of several invariant measures and ergodicity breakingtransitions. We shall present some results concerning the identicationof the ergodic regime and the exponential convergence to equilibriumin this regime. After establishing a connection with monotone cellu-lar automata of bootstrap percolation type, we shall conclude our talkwith a discussion of a particular KCSM for which the correspondingcellular automaton has a peculiar discontinuous percolation transition.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons