Vicious walkers and hook Young tableaux

Kazuhiro Hikami, Takashi Imamura

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of movements of the walker. Applying the saddle point method, we reveal that the scaling limit gives the Tracy-Widom distribution, which is the same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.

Original languageEnglish
Pages (from-to)3033-3048
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number12 SPEC. ISS.
DOIs
Publication statusPublished - Mar 28 2003
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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