TY - JOUR
T1 - The logarithmic derivative for point processes with equivalent Palm measures
AU - Bufetov, Alexander I.
AU - Dymov, Andrey V.
AU - Osada, Hirofumi
N1 - Funding Information:
Clearly, the right-hand side of (3.23) converges as δ → 0 in Lp(Conf(R),Pa), for any p > 0. Together with (3.21)–(3.22), by the Hölder inequality this implies that the numerator of (3.20) converges in L1(Conf(R),Pa) as R → ∞, δ → 0, so that the function Ψb,aR,δShδ> also does. □ Acknowledgements. A. Bufetov’s research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 647133 (ICHAOS)). It has also been funded by the Russian Academic Excellence Project ‘5-100’, the grant MD 5991.2016.1 of the President of the Russian Federation, by RFBR according to the research project 18-31-20031 and by the Gabriel LaméChair at the Chebyshev Laboratory of the SPbSU, a joint initiative of the French Embassy in the Russian Federation and the Saint-Petersburg State University.
Funding Information:
The research of H. Osada was supported by JSPS KAKENHI Grant Number JP16H06338.
Funding Information:
The work of A. Dymov was supported by the Russian Science Foundation under grant 14-21-00162 and performed in Steklov Mathematical Institute of RAS. In conformity with the reglementation of the Russian Science Foundation supporting the research of A. Dymov, we must indicate that A. Dymov prepared Section 3, while A. Bufetov and H. Osada prepared Sections 1, 2 and Appendix A.
Publisher Copyright:
© 2019 The Mathematical Society of Japan.
PY - 2019
Y1 - 2019
N2 - The logarithmic derivative of a point process plays a key role 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 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.
AB - The logarithmic derivative of a point process plays a key role 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 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.
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U2 - 10.2969/jmsj/78397839
DO - 10.2969/jmsj/78397839
M3 - Article
AN - SCOPUS:85067337946
VL - 71
SP - 451
EP - 469
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 2
ER -