Giovedì 11 gennaio 2018 alle ore 15:30
Niccolò Torri (Université Paris 6 - Pierre et Marie Curie)
terrà un seminario dal titolo
"Scaling limit of the prudent random walk"
Aula 3014, Dipartimento di Matematica e Applicazioni (edificio U5, terzo piano, via Cozzi 55, Milano) Università di Milano-Bicocca
Trovate il sommario di seguito. Tutti gli interessati sono invitati a partecipare.
Francesco Caravenna
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The self-interacting self-avoiding random walk (ISAW) is a mathematical model introduced for studying the behavior of a polymer dipped in a repulsive solvent. In this model the possible spatial configurations of the polymer are provided by self-avoiding walk trajectories. However, self avoiding walks, especially in dimension 2 and 3, are complicated objects. This is the reason why, in the mathematical literature, the ISAW model was studied for sub-families of self-avoiding walks, as for instance the partially directed self-avoiding walk. A natural generalization of the partially directed self-avoiding walk is given by the so called "prudent random walk". A prudent path a non-directed self-avoiding path which cannot take a step towards a previously visited lattice site.
The prudent self-avoiding walk has attracted the attention of the combinatorial and probabilistic community over recent years and already the 2-dimensional case presents challenging issues. In this talk we consider two of such issues, concerning the scaling limit as well as exponential growth rate of the set of prudent paths, making a link with the general context of the ISAW model.
Joint work with N. Pétrélis and R. Sun
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Francesco Caravenna
Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca Via Cozzi 55, 20125 Milano, Italy
http://www.matapp.unimib.it/~fcaraven/ _________________________________________