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Title of Journal: Probab Theory Relat Fields

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Abbravation: Probability Theory and Related Fields

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Springer-Verlag

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10.1007/s10531-004-0224-z

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1432-2064

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Markov processes on partitions

Authors: Alexei Borodin Grigori Olshanski
Publish Date: 2005/08/17
Volume: 135, Issue: 1, Pages: 84-152
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Abstract

We introduce and study a family of Markov processes on partitions The processes preserve the socalled zmeasures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group We show that the dynamical correlation functions of these processes have determinantal structure and we explicitly compute their correlation kernels We also compute the scaling limits of the kernels in two different regimes The limit kernels describe the asymptotic behavior of large rows and columns of the corresponding random Young diagrams and the behavior of the Young diagrams near the diagonal

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  2. On the Dirichlet problem for asymmetric zero-range process on increasing domains
  3. Propagation and conditional propagation of chaos for pressureless gas equations
  4. Wasserstein space over the Wiener space
  5. Quasi-stationary distributions for structured birth and death processes with mutations
  6. Outliers in the spectrum of iid matrices with bounded rank perturbations
  7. Product of random projections, Jacobi ensembles and universality problems arising from free probability
  8. Poincaré type inequalities on the discrete cube and in the CAR algebra
  9. The largest eigenvalue of small rank perturbations of Hermitian random matrices
  10. Invariance principle for the random conductance model
  11. Modified logarithmic Sobolev inequalities and transportation inequalities
  12. Asymptotic statistical equivalence for scalar ergodic diffusions
  13. Zero-temperature Glauber dynamics on $${\mathbb{Z}^d}$$
  14. Selector processes on classes of sets
  15. The divergence of Banach space valued random variables on Wiener space
  16. A simple proof of exponential decay of subcritical contact processes
  17. Large deviations for many Brownian bridges with symmetrised initial-terminal condition
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