Timár, Ádám (2023) A Factor Matching of Optimal Tail Between Poisson Processes. COMBINATORICA, 43 (2). pp. 421-427. ISSN 0209-9683
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Abstract
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension d at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., a measurable function of the point configurations that commutes with translations), and with the property that the distance between two matched configuration points has a tail distribution that decays as fast as possible in magnitude, namely, as b exp(−cr d ) with suitable constants b, c > 0. This settles the most difficult version of such matching problems: bicolored (versus unicolored) and deterministic (versus randomized). Our proof relies on two earlier results: an allocation (“land-division”) rule of similar tail for a Poisson point process by Markó and the author, and a recent breakthrough result of Bowen, Kun and Sabok that enables one to obtain perfect matchings from fractional perfect matchings under suitable conditions.
Item Type: | Article |
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Uncontrolled Keywords: | Poisson point process; land division; Factor matching; Allocation rule; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 03 Apr 2024 09:15 |
Last Modified: | 03 Apr 2024 09:15 |
URI: | https://real.mtak.hu/id/eprint/191442 |
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