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CATEGORIES:Probability
SUMMARY:Soliton decomposition of the Box-Ball System - Leo
Rolla (Warwick)
DTSTART;TZID=Europe/London:20210302T140000
DTEND;TZID=Europe/London:20210302T150000
UID:TALK157822AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/157822
DESCRIPTION:The Box-Ball System is a cellular automaton introd
uced by Takahashi and Satsuma as a discrete counte
rpart of the Korteweg & de Vries (KdV) differentia
l equation. Both systems exhibit solitons\, solita
ry waves that conserve shape and speed even after
collision with other solitons. A configuration is
a binary function on the integers representing box
es which may contain one ball or be empty. A carri
er visits successively boxes from left to right\,
picking balls from occupied boxes and depositing o
ne ball\, if carried\, at each visited empty box.
Conservation of solitons suggests that this dynami
cs has many spatially-ergodic invariant measures b
esides the i.i.d. distribution. Building on Takaha
shi-Satsuma identification of solitons\, we provid
e a soliton decomposition of the ball configuratio
ns and show that the dynamics reduces to a hierarc
hical translation of the components\, finally obta
ining an explicit recipe to construct a rich famil
y of invariant measures. We also consider the a.s.
asymptotic speed of solitons of each size. An ext
ended version of this abstract\, references\, simu
lations\, and the slides\, all can be found at htt
ps://mate.dm.uba.ar/~leorolla/bbs-abstract.pdf. Th
is is a joint work with Pablo A. Ferrari\, Chi Ngu
yen\, Minmin Wang.
LOCATION:Zoom
CONTACT:Perla Sousi
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