>>> English version below! <<<

Carə tuttə,

Vi annuncio il prossimo seminario MAP:

--> Speaker: Pavlos Zoubouloglou (University of North Carolina)

--> Data: Giovedì 29 Giugno, ore 14

--> Dove: Aula Seminari del Dipartimento di Matematica (Pisa) e Online su Gmeet: Pavlos Zoubouloglou (seminarimap.wixsite.com)

--> Titolo: Large Deviations for Empirical Measures of Self-Interacting Markov Chains

--> Abstract: Let $\Delta^o$ be a finite set and, for each probability measure $m$ on $\Delta^o$ , let $G(m)$ be a transition kernel on $\Delta^o$ . Consider the sequence $\{X_n\}$ of $\Delta^o$ -valued random variables such that, given $X_0,\ldots,X_n$ , the conditional distribution of $X_{n+1}$ is $G(L^{n+1})(X_n,\cdot)$ , where $L^{n+1}=\frac{1}{n+1}\sum_{i=0}^{n}\delta_{X_i}$ . Under conditions on $G$ we establish a large deviation principle for the sequence $\{L^n\}$ . As one application of this result we obtain large deviation asymptotics for the Aldous-Flannery-Palacios (1988) approximation scheme for quasi-stationary distributions of finite state Markov chains. The conditions on $G$ cover other models as well, including certain models with edge or vertex reinforcement.

--> Arxiv link: https://arxiv.org/abs/2304.01384

Ricordiamo che questi seminari sono aperti a tuttə: la prima metà del seminario introduce i concetti e gli strumenti necessari per la seconda metà, dedicata agli argomenti di ricerca.

Per altre informazioni, visitate il nostro sito:
https://seminarimap.wixsite.com/seminarimap

A presto,

Gli organizzatori:
Daniele Barbera
Jeremy Mirmina
Mario Rastrelli
Leonardo Roveri
Luciano Sciaraffia

- o - o - o - o - o - o - o - o - o - o - o - o - o - o - o -

>>> English Version <<<

Dear all,

Here the announcement of the next MAP seminar:

--> Speaker: Pavlos Zoubouloglou (University of North Carolina)

--> Date: Thursday 29th June, 14:00

--> Where: Aula Seminari, Dipartimento di Matematica (Pisa) and Online on Gmeet: Pavlos Zoubouloglou (seminarimap.wixsite.com)

--> Title: Large Deviations for Empirical Measures of Self-Interacting Markov Chains

--> Abstract: Let $\Delta^o$ be a finite set and, for each probability measure $m$ on $\Delta^o$ , let $G(m)$ be a transition kernel on $\Delta^o$ . Consider the sequence $\{X_n\}$ of $\Delta^o$ -valued random variables such that, given $X_0,\ldots,X_n$ , the conditional distribution of $X_{n+1}$ is $G(L^{n+1})(X_n,\cdot)$ , where $L^{n+1}=\frac{1}{n+1}\sum_{i=0}^{n}\delta_{X_i}$ . Under conditions on $G$ we establish a large deviation principle for the sequence $\{L^n\}$ . As one application of this result we obtain large deviation asymptotics for the Aldous-Flannery-Palacios (1988) approximation scheme for quasi-stationary distributions of finite state Markov chains. The conditions on $G$ cover other models as well, including certain models with edge or vertex reinforcement.

--> Arxiv link: https://arxiv.org/abs/2304.01384

We remind that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

For more information, check our website:

https://seminarimap.wixsite.com/seminarimap

See you soon,

The organizers:

Daniele Barbera
Jeremy Mirmina
Mario Rastrelli
Leonardo Roveri
Luciano Sciaraffia