تقرير
Spatial particle processes with coagulation: Gibbs-measure approach, gelation and Smoluchowski equation
| العنوان: | Spatial particle processes with coagulation: Gibbs-measure approach, gelation and Smoluchowski equation |
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| المؤلفون: | Andreis, Luisa, König, Wolfgang, Langhammer, Heide, Patterson, Robert I. A. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 82C22, 60J25, 60F10, 60G55, 60K35, 35Q70 |
| الوصف: | We study a spatial Markovian particle system with pairwise coagulation, a spatial version of the Marcus--Lushnikov process: according to a coagulation kernel $K$, particle pairs merge into a single particle, and their masses are united. We introduce a statistical-mechanics approach to the study of this process. We derive an explicit formula for the empirical process of the particle configuration at a given fixed time $T$ in terms of a reference Poisson point process, whose points are trajectories that coagulate into one particle by time $T$. The non-coagulation between any two of them induces an exponential pair-interaction, which turns the description into a many-body system with a Gibbsian pair-interaction. Based on this, we first give a large-deviation principle for the joint distribution of the particle histories (conditioning on an upper bound for particle sizes), in the limit as the number $N$ of initial atoms diverges and the kernel scales as $\frac 1N K$. We characterise the minimiser(s) of the rate function, we give criteria for its uniqueness and prove a law of large numbers (unconditioned). Furthermore, we use the unique minimiser to construct a solution of the Smoluchowski equation and give a criterion for the occurrence of a gelation phase transition. Comment: 60 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.06668 |
| رقم الأكسشن: | edsarx.2401.06668 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |