Journal of the Mathematical Society of Japan

The logarithmic derivative for point processes with equivalent Palm measures

Alexander I. BUFETOV, Andrey V. DYMOV, and Hirofumi OSADA

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Abstract

The logarithmic derivative of a point process plays a key rôle in the general approach, due to the third author, to constructing diffusions preserving a given point process. In this paper we explicitly compute the logarithmic derivative for determinantal processes on $\mathbb{R}$ with integrable kernels, a large class that includes all the classical processes of random matrix theory as well as processes associated with de Branges spaces. The argument uses the quasi-invariance of our processes established by the first author.

Article information

Source
J. Math. Soc. Japan, Volume 71, Number 2 (2019), 451-469.

Dates
Received: 6 July 2017
Revised: 17 October 2017
First available in Project Euclid: 4 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1551690078

Digital Object Identifier
doi:10.2969/jmsj/78397839

Mathematical Reviews number (MathSciNet)
MR3943446

Subjects
Primary: 60G55: Point processes
Secondary: 60J60: Diffusion processes [See also 58J65]

Keywords
point processes determinantal processes logarithmic derivative infinite-dimensional diffusion Palm measure

Citation

BUFETOV, Alexander I.; DYMOV, Andrey V.; OSADA, Hirofumi. The logarithmic derivative for point processes with equivalent Palm measures. J. Math. Soc. Japan 71 (2019), no. 2, 451--469. doi:10.2969/jmsj/78397839. https://projecteuclid.org/euclid.jmsj/1551690078


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