Infinite-dimensional diffusions as limits of random walks on partitions

By Alexei Borodin, Grigori Olshanski. 2007

65 citations recorded by the source corpus.

Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c3804140f3d4af9a7d540771273d6d795e11b030

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. L. Petrov
2. Alexei Borodin
3. Grigori Olshanski
4. Ivan Corwin
5. Philippe Biane

In Statistics and Probability

1. L. Petrov
2. Alexei Borodin
3. Grigori Olshanski
4. Ivan Corwin
5. Jeremy Quastel
6. P. Ferrari
7. Philippe Biane

Citations in the corpus

• Representations of the Infinite Symmetric Group (2016, background): “• Models of Markov dynamics of representation-theoretic origin: Borodin and Olshanski [17], [19], [20], [21], Olshanski [94], [95], — Acknowledgments.”
• Two-parameter family of infinite-dimensional diffusions on the Kingman simplex (2007, methodology): “Monomial symmetric functions in the present paper play the same role as Schur functions in [2].”