Il giorno 21 febbraio 2017 presso l'Aula E del Dipartimento di Matematica, Sapienza Università di Roma
si terranno i seguenti seminari di Probabilità e Statistica Matematica:
Ore 14.30 Wolfgand Woess (TU Graz, Austria)
Multidimensional reflected random walk - some results and many questions
Abstract: Let (Y_n,V_n) be i.i.d. distributed, with the components r and s-dimensional, respectively.
Reflected random walk starting at a point x of the positive r-dimensional orthant is defined recursively by X_0 = x, X_n = |X_{n−1}−Y_n|, where |(a_1,...,a_r)| = (|a_1|,...,|a_r|).
In R^s, consider the ordinary sum S_n = V_1 +···+V_n . We are interested in (topological) recurrence of the process (X_n,v+S_n) starting at (x,v).
While this is quite well understood for refelcted random walk with r=1, in higher dimension (r \geq 2) or with some non-reflected coordinates (s \in {1,2})
we have a few basic results and various open questions with some partial answers. This is work with Judith Kloas, with input from Marc Peigne' and Wojciech Cygan.
Ore 15.30 Oriane Blondel (CNRS Lyon, France)
More random walks on random walks
Abstract: We consider a Poissonian distribution of particles performing independent
simple random walks. Simultaneously, on top of this system, a random walker
evolves with a drift to the right when it is on top of (at least) a particle, to the
left when it is on an empty site. We obtain a LLN, CLT and large deviation
bounds in high and low density. Joint work with Marcelo Hilario, Renato dos Santos,
Vladas Sidoravicius, Augusto Teixeira.