Noticias en español
Unraveling parking on random trees via random graphs.
Abstract: Imagine a plane tree together with a configuration of particles (cars) at each vertex.Each car tries to park on its node, and if the latter is occupied, it moves downward towards the root trying to find an empty slot.When the underlying plane tree is a critical Galton–Watson conditioned to be large, and when the cars arrivals are i.i.d. on each vertex, we observe a phase transition:- when the density of cars is small enough, all but a few manage to park safely,- whereas when the density of cars is high enough, a positive fraction of them do not manage to park and exit through...
Read MoreA mean-field theory for certain deep neural networks
Abstract: A natural approach to understand overparameterized deep neural networks is to ask if there is some kind of natural limiting behavior when the number of neurons diverges. We present a rigorous limit result of this kind for networks with complete connections and “random-feature-style” first and last layers. Specifically, we show that network weights are approximated by certain “ideal particles” whose distribution and dependencies are described by McKean-Vlasov mean-field model. We will present the intuition behind our approach; sketch some of the key technical...
Read MoreRandom time transformation analysis of Covid19 2020.
Abstract: The SIR epidemiological equations model new affected and removed cases as roughly proportional to the current number of infected cases. An alternative that has been considered in the literature will be adopted, in which the number of new affected cases is proportional to the α power of the number of infected cases. After arguing that α =1 models exponential growth while α <1 models polynomial growth, a simple method for parameter estimation in differential equations subject to noise, the random-time transformation RTT of Bassan, Meilijson, Marcus and Talpaz 1997, will be...
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