## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 119 - 128

### Non-Markov property of certain eigenvalue processes analogous to Dyson's model

Ryoki Fukushima, Atsushi Tanida, and Kouji Yano

#### Abstract

It is proven that the eigenvalue process of Dyson's random matrix process of size two becomes non-Markov if the common coefficient $1/\sqrt{2}$ in the non-diagonal entries is replaced by a different positive number.

#### Article information

**Source***Probabilistic Approach to Geometry*, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 119-128

**Dates**

Received: 14 January 2009

Revised: 5 March 2009

First available in Project Euclid:
24 November 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1543086314

**Digital Object Identifier**

doi:10.2969/aspm/05710119

**Mathematical Reviews number (MathSciNet)**

MR2605413

**Zentralblatt MATH identifier**

1200.60011

**Subjects**

Primary: 15A52 60-06: Proceedings, conferences, collections, etc. 60J65: Brownian motion [See also 58J65] 60J99: None of the above, but in this section

**Keywords**

Non-Markov property random matrix eigenvalue process Dyson's model beta-ensembles

#### Citation

Fukushima, Ryoki; Tanida, Atsushi; Yano, Kouji. Non-Markov property of certain eigenvalue processes analogous to Dyson's model. Probabilistic Approach to Geometry, 119--128, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710119. https://projecteuclid.org/euclid.aspm/1543086314