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The intertwining property for $\beta $-Laguerre processes and integral operators for Jack polynomials
Yosuke Kawamato, Genki Shibukawa
https://arxiv.org/abs/2505.23139

The intertwining property for $β$-Laguerre processes and integral operators for Jack polynomials
The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature $β\ge 1$ and parameter $α>-1$. We introduce a Markov kernel that depends on both $β$ and $ α$, and establish new intertwining relations for the $β$-Laguerre processes using this kernel. A key observation is that Jack symmetric polynomials are eigenfunctions of our Markov kernel, which allows us to apply a method established by Ramanan and Shkolnikov. Additionally, as a by-product, we deri…

This https://arxiv.org/abs/2205.07214 has been replaced.
link: https://scholar.google.com/scholar?q=a

Entropy Production for Discrete-Time Markov Processes
We study the multiple definitions of the entropy production for discrete-time Markov processes in single systems and composite systems. These definitions have been studied in single systems, but less so in composite systems. With a clear distinction, we review the equivalence condition and the meaning of the multiple definitions and show that all definitions satisfy the important property for the entropy production, such as non-negativity. We also show that the inequalities between total entrop…

This https://arxiv.org/abs/2505.14762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiple radial SLE($κ$) and quantum Calogero-Sutherland system
In this first of two articles, we study the multiple radial $\mathrm{SLE}(κ)$ systems with parameter $κ> 0$ -- a family of random multi-curve systems in a simply-connected domain $Ω$, with marked boundary points $z_1, \ldots, z_n \in \partial Ω$ and a marked interior point $q$. As a consequence of the domain Markov property and conformal invariance, we show that such systems are characterized by equivalence classes of partition functions, which are not necessarily conformally covariant. Nev…