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SUMMARY:Soliton decomposition of the Box-Ball System - Leo Rolla (Warwick)
DTSTART:20210302T140000Z
DTEND:20210302T150000Z
UID:TALK157822@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The Box-Ball System is a cellular automaton introduced by Taka
 hashi and Satsuma as a discrete counterpart of the Korteweg & de Vries (Kd
 V) differential equation. Both systems exhibit solitons\, solitary waves t
 hat conserve shape and speed even after collision with other solitons. A c
 onfiguration is a binary function on the integers representing boxes which
  may contain one ball or be empty. A carrier visits successively boxes fro
 m left to right\, picking balls from occupied boxes and depositing one bal
 l\, if carried\, at each visited empty box. Conservation of solitons sugge
 sts that this dynamics has many spatially-ergodic invariant measures besid
 es the i.i.d. distribution. Building on Takahashi-Satsuma identification o
 f solitons\, we provide a soliton decomposition of the ball configurations
  and show that the dynamics reduces to a hierarchical translation of the c
 omponents\, finally obtaining an explicit recipe to construct a rich famil
 y of invariant measures. We also consider the a.s. asymptotic speed of sol
 itons of each size. An extended version of this abstract\, references\, si
 mulations\, and the slides\, all can be found at https://mate.dm.uba.ar/~l
 eorolla/bbs-abstract.pdf. This is a joint work with Pablo A. Ferrari\, Chi
  Nguyen\, Minmin Wang.
LOCATION:Zoom
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