Title: Dynamics of the Box-ball System With Random Initial Conditions Via Pitman's Transformation
Publisher: Amer Mathematical Society
Publication Date: 2023
Language: English
ISBN 10: 1470456338
ISBN 13: 9781470456337
Binding: Paperback
Condition: Brand New
Weight: 0.27 kilograms

About this title

Synopsis

"The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a model, Ferrari et al. recently showed the invariance in distribution of Bernoulli product measures with density strictly less than 1/2 , and gave a soliton decomposition for invariant measures more generally. We study the BBS dynamics using the transformation ofa nearest neighbour path encoding of the particle configuration given by 'reflection in the past maximum', which was famously shown by Pitman to connect Brownian motion and a three-dimensional Bessel process. We use this to characterise the set of configurations for which the dynamics are well-defined and reversible (i.e. can be inverted) for all times. The techniques developed to understand the deterministic dynamics are subsequently applied to study the evolution of the BBS from a random initial configuration. Specifically, we give simple sufficient conditions for random initial conditions to be invariant in distribution under the BBS dynamics, which we check in several natural examples, and also investigate the ergodicity of the relevant transformation. Furthermore, we analyse various probabilistic properties of the BBS that are commonly studied for interacting particle systems, such as the asymptotic behavior of the integrated current of particles and of a tagged particle. Finally, for Bernoulli product measures with parameter p [up arrow] 1/2 (which may be considered the 'high density' regime), the path encoding we consider has a natural scaling limit, which motivates the introduction of a new continuous version of the BBS that we believe will be ofindependent interest as a dynamical system"--

"About this title" may belong to another edition of this title.

Store Description

Visit Seller's Storefront

Seller's business information

Edward Bowditch Ltd
Exstowe, Exton, Exeter, EX3 0PP, United Kingdom

Sale & Shipping Terms

Terms of Sale

Legal entity name: Edward Bowditch Ltd
Legal entity form: Limited company
Business correspondence address: Exstowe, Exton, Exeter, EX3 0PP
Company registration number: 04916632
VAT registration: GB834241546
Authorised representative: Mr. E. Bowditch

Shipping Terms

Orders usually dispatched within two working days. Please note that at this time all domestic United Kingdom orders are sent by trackable UPS courier, we choose not to offer a lower cost alternative.

Shipping rates from United Kingdom to U.S.A.

Shipping rates from United Kingdom to U.S.A.
Order quantity	7 to 14 business days	2 to 3 business days
First item	US$ 13.30	US$ 33.25

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.