{"title":"聚结-破碎Wasserstein动力学中的粒子数","authors":"V. Konarovskyi","doi":"10.37863/tsp-2295310746-81","DOIUrl":null,"url":null,"abstract":"\nWe consider the system of sticky-reflected Brownian particles on the real line proposed in [4]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the mass which they transfer. It is known that the system consists of a finite number of distinct particles for almost all times. In this paper, we show that the system also admits an infinite number of distinct particles on a dense subset of the time interval if and only if the function responsible for the splitting of particles takes an infinite number of values. \n","PeriodicalId":38143,"journal":{"name":"Theory of Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On number of particles in coalescing-fragmentating Wasserstein dynamics\",\"authors\":\"V. Konarovskyi\",\"doi\":\"10.37863/tsp-2295310746-81\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\nWe consider the system of sticky-reflected Brownian particles on the real line proposed in [4]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the mass which they transfer. It is known that the system consists of a finite number of distinct particles for almost all times. In this paper, we show that the system also admits an infinite number of distinct particles on a dense subset of the time interval if and only if the function responsible for the splitting of particles takes an infinite number of values. \\n\",\"PeriodicalId\":38143,\"journal\":{\"name\":\"Theory of Stochastic Processes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Stochastic Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37863/tsp-2295310746-81\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Stochastic Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37863/tsp-2295310746-81","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
On number of particles in coalescing-fragmentating Wasserstein dynamics
We consider the system of sticky-reflected Brownian particles on the real line proposed in [4]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the mass which they transfer. It is known that the system consists of a finite number of distinct particles for almost all times. In this paper, we show that the system also admits an infinite number of distinct particles on a dense subset of the time interval if and only if the function responsible for the splitting of particles takes an infinite number of values.
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