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Large deviations for a spatial particle process with coagulation

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Dipartimento di Matematica Guido Castelnuovo, Università Sapienza Roma

In this talk we consider a spatial version of the Marcus-Lushnikov process, which models the evolution of particles that merge pairwise in a series of coagulation events. The particles are equipped with a spatial location and an integer mass. In a coagulation event a pair of particles is merged and replaced by a new particle. The mass of the newly formed particle is the sum of the former two and its location is sampled according to a given distribution. The exponential rate of a coagulation event depends on the locations and masses of the particle pair via a coagulation kernel. For the non-spatial version of this model it is known that certain kernels exhibit a gelation phase transition, which describes the formation of one or several large particles after a finite time. In this talk we introduce a new approach for studying the process. We will provide a formula that connects its distribution to a Poisson point process and show how this can be used to derive a large deviation principle. From this we gain new insights into the limiting behavior of the process and obtain criteria for the gelation phase transition. (finanziato dall’Unione europea – Next Generation EU)

Speaker ed affiliazione

Heide Langhammer (Weierstrass Institute for Applied Analysis and Stochastics, Berlin )

Contatti/Organizzatori

basile@mat.uniroma1.it

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