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The logarithmic derivative for point processes with equivalent Palm measures. (English) Zbl 1478.60147

Summary: 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.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J60 Diffusion processes
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