Duality between box-ball systems of finite box and/or carrier capacity (Stochastic Analysis on Large Scale Interacting Systems)

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  • Croydon, David A.
    Department of Advanced Mathematical Sciences, Graduate School of Informatics, Kyoto University
  • 佐々田, 槙子
    Graduate School of Mathematical Sciences, University of Tokyo

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抄録

We construct the dynamics of the box-ball system with box capacity J and carrier capacity K, which we abbreviate to BBS(J, K), in the case of infinite initial configurations, and show that this system is dual to the analogous BBS(K, J) model. Towards this end, we build on previous work for the original box-ball system, that is BBS(1, ∞), to show that when the box capacity J and carrier capacity K satisfy J < K the dynamics can be represented by a Pitman- type transformation. These ideas are applied in the case of random initial configurations to show that the distributional properties of spatial stationarity and invariance under the BBS dynamics are dual. Moreover, for independent and identically distributed configurations, we derive a characterisation of invariant measures in terms of a detailed balance equation, which captures the duality of the system locally; this is used to find all invariant measures in this class. Finally, we deduce the speed of a tagged particle, and show that this also satisfies a natural duality relation.

"Stochastic Analysis on Large Scale Interacting Systems". November 5-8, 2018. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Hirofumi Osada and Kenkichi Tsunoda. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

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詳細情報 詳細情報について

  • CRID
    1050287685024473856
  • NII論文ID
    120006950537
  • NII書誌ID
    AA12196120
  • ISSN
    18816193
  • HANDLE
    2433/260645
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • IRDB
    • CiNii Articles

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