Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 78 tok/s
Gemini 2.5 Pro 52 tok/s Pro
GPT-5 Medium 24 tok/s Pro
GPT-5 High 26 tok/s Pro
GPT-4o 120 tok/s Pro
Kimi K2 193 tok/s Pro
GPT OSS 120B 459 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

Determinantal point processes with J-Hermitian correlation kernels (1104.4917v4)

Published 26 Apr 2011 in math.PR

Abstract: Let X be a locally compact Polish space and let m be a reference Radon measure on X. Let $\Gamma_X$ denote the configuration space over X, that is, the space of all locally finite subsets of X. A point process on X is a probability measure on $\Gamma_X$. A point process $\mu$ is called determinantal if its correlation functions have the form $k{(n)}(x_1,\ldots,x_n)=\det[K(x_i,x_j)]_{i,j=1,\ldots,n}$. The function K(x,y) is called the correlation kernel of the determinantal point process $\mu$. Assume that the space X is split into two parts: $X=X_1\sqcup X_2$. A kernel K(x,y) is called J-Hermitian if it is Hermitian on $X_1\times X_1$ and $X_2\times X_2$, and $K(x,y)=-\overline{K(y,x)}$ for $x\in X_1$ and $y\in X_2$. We derive a necessary and sufficient condition of existence of a determinantal point process with a J-Hermitian correlation kernel K(x,y).

Summary

We haven't generated a summary for this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.