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UID:5386@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20241213T110000
DTEND;TZID=Europe/Paris:20241213T120000
DTSTAMP:20241204T152519Z
URL:https://www.i2m.univ-amu.fr/evenements/seminaire-rauzy-2024-12-13/
SUMMARY:Solène Esnay (I2M): Bootstrap Percolation on Rhombus Tilings
DESCRIPTION:Solène Esnay: In this talk\, we introduce dynamical (bootstrap
 ) percolation\, where a tiling of the plane has each tile independently co
 lored 0 or 1 following a measure mu\; then the 1 state propagates step by 
 step to tiles adjacent to at least two 1-colored tiles. We are interested 
 in the asymptotic behavior of this system\, which is a cellular automaton 
 with a spreading 1 state: is the entire tiling asymptotically invaded by 1
 s from mu-almost every initial configuration?\nWe answer this question pos
 itively for a wide variety of tilings (all rhombus tilings\, with a focus 
 during the presentation on Penrose tilings) and measures (a large class th
 at includes nontrivial Bernoulli measures). We do so with a careful study 
 of what stable non-invading patches of 1s would look like\, then with prob
 abilistic arguments as to why this situation mu-almost never happens.
CATEGORIES:Séminaire,Rauzy
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20241027T020000
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