Limiting directions for random walks in classical affine Weyl groups

• Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

random walk

affine Weyl groups

limiting direction

Bn

Cn

Dn

Kac labels

TASEP

multispecies

Mathematics

Matematik

Publikations- och innehållstyp

vet (ämneskategori)

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