Intertwinings for General $$\beta $$ β -Laguerre and $$\beta $$ β -Jacobi Processes

Theodoros Assiotis ()
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Theodoros Assiotis: University of Warwick

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1880-1891

Abstract: Abstract We show that, for $$\beta \ge 1$$ β ≥ 1 , the semigroups of $$\beta $$ β -Laguerre and $$\beta $$ β -Jacobi processes of different dimensions are intertwined in analogy to a similar result for $$\beta $$ β -Dyson Brownian motion recently obtained in Ramanan and Shkolnikov (Intertwinings of $$\beta $$ β -Dyson Brownian motions of different dimensions, 2016. arXiv:1608.01597 ). These intertwining relations generalize to arbitrary $$\beta \ge 1$$ β ≥ 1 the ones obtained for $$\beta =2$$ β = 2 in Assiotis et al. (Interlacing diffusions, 2016. arXiv:1607.07182 ) between h-transformed Karlin–McGregor semigroups. Moreover, they form the key step toward constructing a multilevel process in a Gelfand–Tsetlin pattern leaving certain Gibbs measures invariant. Finally, as a by-product, we obtain a relation between general $$\beta $$ β -Jacobi ensembles of different dimensions.

Keywords: Random matrices; Stochastic processes; Integrable probability; 60H10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0842-0

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