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Bootstrap percolation and kinetically constrained spin models: critical lengths and mixing time scales
http://sms.cam.ac.uk/media/2284386
Martinelli, F (Università degli Studi Roma Tre)
Wednesday 13th July 2016  09:45 to 10:30
40
Bootstrap percolation and kinetically constrained spin models: critical lengths and mixing time scales
http://sms.cam.ac.uk/media/2284386
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Bootstrap percolation and kinetically constrained spin models: critical lengths and mixing time scales
ucs_sms_2283481_2284386
http://sms.cam.ac.uk/media/2284386
Bootstrap percolation and kinetically constrained spin models: critical lengths and mixing time scales
Martinelli, F (Università degli Studi Roma Tre)
Wednesday 13th July 2016  09:45 to 10:30
Tue, 19 Jul 2016 17:07:14 +0100
Isaac Newton Institute
Martinelli, F
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Martinelli, F (Università degli Studi Roma Tre)
Wednesday 13th July 2016 ...
Martinelli, F (Università degli Studi Roma Tre)
Wednesday 13th July 2016  09:45 to 10:30
Cambridge University
2759
http://sms.cam.ac.uk/media/2284386
Bootstrap percolation and kinetically constrained spin models: critical lengths and mixing time scales
Martinelli, F (Università degli Studi Roma Tre)
Wednesday 13th July 2016  09:45 to 10:30
Coauthors: Cristina Toninelli (Univ Paris VII Diderot), Rob Morris (IMPA)
In recent years, a great deal of progress has been made in understanding the behaviour of a particular class of monotone cellular automata, commonly known as bootstrap percolation. In particular, if one considers only twodimensional automata, then we now have a fairly precise understanding of the typical evolution of these processes, starting from prandom initial conditions of infected sites. Given a bootstrap model, one can consider the associated kinetically constrained spin model in which the state (infected or healthy) of a vertex is resampled (independently) at rate 1 by tossing a pcoin if it could be infected in the next step by the bootstrap process, and remains in its current state otherwise. Here p is the probability of infection. The main interest in KCM’s stems from the fact that, as p → 0, they mimic some of the most striking features of the glass transition, a major and still largely open problem in condensed matter physics. In this talk, motivated by recent universality results for bootstrap percolation, I’ll discuss some “universality conjectures” concerning the growth of the (random) infection time of the origin in a KCM as p → 0. Joint project with R. Morris (IMPA) and C. Toninelli (Paris VII),
20160719T17:07:14+01:00
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