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Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces
Branching processes difference-differential equations hyperbolic Brownian motion hyperbolic trigonometry
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2011/9/20
Abstract: A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is examined. Each particle can split in...
Modeling Flocks and Prices: Jumping Particles with an Attractive Interaction
Competing particles center of mass mean field evolution traveling wave fluid limit extreme value statistics
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2011/9/13
Abstract: We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle ...