Interacting particle models and the Pieri-type formulas : the symplectic case with non equal weights

Manon Defosseux (Université Paris Descartes)

Abstract


This paper studies a particle model  connected to a Pieri-type formula for the symplectic compact group. Particles evolve independently apart from a blocking and pushing interaction such that they remain in the set of symplectic Gelfand-Tsetlin patterns. We show that if only one row of the patterns is considered, one obtains a symplectic Schur process. The model leads in particular to the particle model with a wall defined by Jon Warren and Peter Windridge and to a matrix model previously studied by the author.

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Pages: 1-12

Publication Date: July 24, 2012

DOI: 10.1214/ECP.v17-2193

References

  • Alexei Borodin and Patrik Ferrari. Anisotropic growth of random surfaces in 2+1 dimensions, ARXIV0804.3035v2.
  • Borodin, Alexei; Kuan, Jeffrey. Random surface growth with a wall and Plancherel measures for $\rm O(\infty)$. Comm. Pure Appl. Math. 63 (2010), no. 7, 831--894. MR2662425
  • Defosseux, Manon. Orbit measures, random matrix theory and interlaced determinantal processes. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 1, 209--249. MR2641777
  • Manon Defosseux. An interacting particles model and a Pieri-type formula for the orthogonal group, ARXIV1012.0117.
  • Knapp, Anthony W. Lie groups beyond an introduction. Second edition. Progress in Mathematics, 140. Birkhäuser Boston, Inc., Boston, MA, 2002. xviii+812 pp. ISBN: 0-8176-4259-5 MR1920389
  • Rogers, L. C. G.; Pitman, J. W. Markov functions. Ann. Probab. 9 (1981), no. 4, 573--582. MR0624684
  • Warren, Jon; Windridge, Peter. Some examples of dynamics for Gelfand-Tsetlin patterns. Electron. J. Probab. 14 (2009), no. 59, 1745--1769. MR2535012
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