{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T23:57:22Z","timestamp":1772495842537,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T00:00:00Z","timestamp":1690243200000},"content-version":"vor","delay-in-days":115,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"ELKH Alfr\u00e9d R\u00e9nyi Institute of Mathematics"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension <jats:italic>d<\/jats:italic> 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$b\\exp (-cr^d)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>b<\/mml:mi>\n                    <mml:mo>exp<\/mml:mo>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mi>c<\/mml:mi>\n                    <mml:msup>\n                      <mml:mi>r<\/mml:mi>\n                      <mml:mi>d<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with suitable constants <jats:inline-formula><jats:alternatives><jats:tex-math>$$b,c&gt;0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>b<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>c<\/mml:mi>\n                    <mml:mo>&gt;<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. 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 (\u201cland-division\u201d) rule of similar tail for a Poisson point process by Mark\u00f3 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.<\/jats:p>","DOI":"10.1007\/s00493-023-00051-6","type":"journal-article","created":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T11:01:52Z","timestamp":1690282912000},"page":"421-427","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Factor Matching of Optimal Tail Between Poisson Processes"],"prefix":"10.1007","volume":"43","author":[{"given":"\u00c1d\u00e1m","family":"Tim\u00e1r","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,7,25]]},"reference":[{"key":"51_CR1","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/BF02579135","volume":"4","author":"M Ajtai","year":"1984","unstructured":"Ajtai, M., Koml\u00f3s, J., Tusn\u00e1dy, G.: On optimal matchings. 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