Dear colleagues,
We are happy to announce the following *hybrid* - that is, in person with online streaming - *talks*:
Speaker: *Guangqu Zheng* (University of Liverpool) Title: CLT and almost sure CLT for hyperbolical Anderson model with Lévy noise. (Abstract below.)
Speaker: *Gidi Amir* (Bar Ilan University) Title: Speed, entropy and other quantities of random walks on groups. (Abstract below.)
Date and time: *Tuesday October 10, 10:30-12:30 (Rome time zone) * Place: Dept. of Mathematics and Applications, *Università di Milano-Bicocca*, *room 3014* (*U5/RATIO* building).
*Webex meeting link*: https://unimib.webex.com/unimib-it/j.php?MTID=md61ac6bd0a0c3288815a386b472b4...
*ID meeting*: 2741 951 7655 *Password*: mwCpfq3tr54 - *Abstract (Zheng)*. In this talk, we will first briefly mention the recent research on CLT results of random field solutions to stochastic heat equations and stochastic wave equations with various Gaussian noises. Then, we will talk about the spatial ergodicity (first order result) and CLT (second order fluctuation) for a stochastic linear wave equation driven by Lévy noise, which is based on a joint work with R. Balan (Ottawa) [arXiv:2302.14178]. Finally, we will talk about the associated almost sure central limit theorem, based on a joint work with R. Balan (Ottawa) and P. Xia (Auburn).
*Abstract (Amir)*. Given a (finitely supported, symmetric) random walk X_n on a countable groups G, one may consider several quantities associated to the random walk, such as the expected distance E|X_n|, its Shannon entropy H(X_n), its return probabilities P(X_n=id) and more. For example, on polynomial growth groups (e.g. Z^d) it is well known the walk is always diffusive, has logarithmic entropy and polynomial decaying return probabilities, while on the free group the speed and entropy of a random walk increase linearly with n and the return probabilities decay exponentially. A natural problem is to understand what are the possible range of behaviours of such quantities for random walks on groups and how they relate to other group properties. In this lecture I will survey some old and new results on the subject, including some more recent works on speed and entropy of random walks on intermediate growth groups and on possible behaviours of the Law of Iterated Logarithm. The talk is based on joint works with B. Virag, G. Blachar, C. Saroussi and T. Zheng, though we will also touch upon works by A. Erschler, and by J. Brieussel and T. Zheng. All notions will be defined in the talk, and in particular no knowledge of groups is required for the talk. - These talks are part of the *(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico.
Participation is free and welcome!
Best regards, The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)
Dear colleagues,
The *second talk* (by Gidi Amir, Bar Ilan University) *has been canceled* due to unforeseen circumstances and will be postponed to a later date.
The *first talk* (by Guangqu Zheng, University of Liverpool) *is confirmed* (Tomorrow - Tuesday 10 Oct, 10:30-11:30 Rome time zone).
Best regards, The organizers
Il giorno mer 4 ott 2023 alle ore 10:06 Maurizia Rossi < maurizia.rossi@unimib.it> ha scritto:
Dear colleagues,
We are happy to announce the following *hybrid* - that is, in person with online streaming - *talks*:
Speaker: *Guangqu Zheng* (University of Liverpool) Title: CLT and almost sure CLT for hyperbolical Anderson model with Lévy noise. (Abstract below.)
Speaker: *Gidi Amir* (Bar Ilan University) Title: Speed, entropy and other quantities of random walks on groups. (Abstract below.)
Date and time: *Tuesday October 10, 10:30-12:30 (Rome time zone) * Place: Dept. of Mathematics and Applications, *Università di Milano-Bicocca*, *room 3014* (*U5/RATIO* building).
*Webex meeting link*: https://unimib.webex.com/unimib-it/j.php?MTID=md61ac6bd0a0c3288815a386b472b4...
*ID meeting*: 2741 951 7655 *Password*: mwCpfq3tr54
*Abstract (Zheng)*. In this talk, we will first briefly mention the recent research on CLT results of random field solutions to stochastic heat equations and stochastic wave equations with various Gaussian noises. Then, we will talk about the spatial ergodicity (first order result) and CLT (second order fluctuation) for a stochastic linear wave equation driven by Lévy noise, which is based on a joint work with R. Balan (Ottawa) [arXiv:2302.14178]. Finally, we will talk about the associated almost sure central limit theorem, based on a joint work with R. Balan (Ottawa) and P. Xia (Auburn).
*Abstract (Amir)*. Given a (finitely supported, symmetric) random walk X_n on a countable groups G, one may consider several quantities associated to the random walk, such as the expected distance E|X_n|, its Shannon entropy H(X_n), its return probabilities P(X_n=id) and more. For example, on polynomial growth groups (e.g. Z^d) it is well known the walk is always diffusive, has logarithmic entropy and polynomial decaying return probabilities, while on the free group the speed and entropy of a random walk increase linearly with n and the return probabilities decay exponentially. A natural problem is to understand what are the possible range of behaviours of such quantities for random walks on groups and how they relate to other group properties. In this lecture I will survey some old and new results on the subject, including some more recent works on speed and entropy of random walks on intermediate growth groups and on possible behaviours of the Law of Iterated Logarithm. The talk is based on joint works with B. Virag, G. Blachar, C. Saroussi and T. Zheng, though we will also touch upon works by A. Erschler, and by J. Brieussel and T. Zheng. All notions will be defined in the talk, and in particular no knowledge of groups is required for the talk.
These talks are part of the *(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico.
Participation is free and welcome!
Best regards, The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)
-- Maurizia Rossi
Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca https://mauriziarossi.wordpress.com
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Maurizia Rossi