Abstract
Probability evolution for complex multi-linear non-local interactions
Irene Gamba
University of Texas at Austin
We present a generalized formulation of kinetic non-local models of collisional type that cover a large class of global energy dissipative
phenomena, such as those of inelastic collisions, mixtures and slowdown cooling processes, economics and social dynamics; in the setting of
multiplicatively interactive stochastic processes.
The working framework lays in the space of characteristic functions of probabilities measures for a class of equations of non-local multi linear form, where is possible to recover the longtime dynamics as those of (W)_2 metric evolution to stable or dynamically stable states self-similar) for finite energy; but also the technique extends
them to cases of infinity energy initial data, where the classical definition of W_2 metric does not apply. One of the consequences is the existence and characterization of the dynamically
stable (self-similar) states in probability space which can not have all moments bounded and even may admit singularities at the origin, while remaining integrable (as in examples of limit mixture models for a slow-down process). Part of this work has been in collaboration with A. Bobylev and C. Cergignani
phenomena, such as those of inelastic collisions, mixtures and slowdown cooling processes, economics and social dynamics; in the setting of
multiplicatively interactive stochastic processes.
The working framework lays in the space of characteristic functions of probabilities measures for a class of equations of non-local multi linear form, where is possible to recover the longtime dynamics as those of (W)_2 metric evolution to stable or dynamically stable states self-similar) for finite energy; but also the technique extends
them to cases of infinity energy initial data, where the classical definition of W_2 metric does not apply. One of the consequences is the existence and characterization of the dynamically
stable (self-similar) states in probability space which can not have all moments bounded and even may admit singularities at the origin, while remaining integrable (as in examples of limit mixture models for a slow-down process). Part of this work has been in collaboration with A. Bobylev and C. Cergignani
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