An inhomogeneous multispecies TASEP on a ring

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in differen...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 57; pp. 21 - 43
Main Authors Ayyer, Arvind, Linusson, Svante
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2014
Subjects
Bully paths
Complete homogeneous symmetric polynomials
Exclusion process
Lumping
Mathematical analysis
Multiline queues
Multispecies particles
Proving
Queues
Lumping
Multispecies particles
60K35
05A05
Bully paths
Multiline queues
Complete homogeneous symmetric polynomials
Exclusion process
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Summary:We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove Lam and Williams' conjectures in two special cases by generalizing the rates of the Ferrari–Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0196-8858
1090-2074
1090-2074
DOI:10.1016/j.aam.2014.02.001