Segnalo il seguente seminario, che si terrà Giovedì prossimo in Sapienza.
Notare il giorno e l'aula inusuali.
*Giovedì 27 Aprile, ore 14:00* Aula L, Dipartimento di Matematica, Sapienza
Università di Roma
*Speaker:* Gérard Letac (Paul Sabatier University - Toulouse III)
*Title: *From the Matsumoto Yor observation to stationary measures for a
discrete KdV model
*Abstract: *Let
F(x,y)=(u,v) from R2 into itself such that F∘F(x,y)=(x,y). The discrete
Korteweg-de Vries model associated to F considers two dimensional vectors (x
tn,ytn) indexed by (t,n)∈Z2 submitted to (xtn,ytn)=F(xt−1n,ytn−1). In the
particular case F(x,y)=(y−1−(x+y)−1,(x+y)−1), by considerations on Brownian
motion, Matsumoto-Yor in 1999 have found laws of independent random
variables X,Y such that U,V defined by F(X,Y)=(U,V) are independent,
obtaining stationary measures on the KdV model. In an extraordinary paper,
Croydon and Sasada (2021) have generalized this result to the surprizing F(x
,y)=(yβxy+1αxy+1,xαxy+1βxy+1). The lecture will prove that if X,Y are
independent and such that U,V=F(X,Y) are also independent, then the laws of
X and Y are indeed the generalized Gaussian distributions discovered by
Croydon and Sasada. This is joint work with Jacek Wesolowski (arXiv
2203.05404).
*Nota*: Sul sito del dipartimento il seminario è, ad oggi, annunciato per
le 17:00 (in Aula II), ma si terrà alle 14:00 (in Aula L), come annunciato
in questa email. La pagina è in corso di aggiornamento.
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Vittoria Silvestri
Assistant Professor
Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome
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