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<DIV><FONT face=Arial size=2>Gentile prof./dott.,</FONT></DIV>
<DIV><FONT face=Arial size=2>la avvertiamo che nei prossimi giorni alla Scuola
Normale si terrà il seguente seminario di matematica nell'ambito del Colloquio
De Giorgi:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Giovedì 5 Maggio 2003, in aula Mancini alle ore
15:00,</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Prof. Gérard Ben Arous</STRONG> - Ecole
Polytechnique Federale de Lausanne</FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>"Random Media: when homogenization is not
enough".<BR></FONT><FONT face=Arial size=2>Joint work with S.Molchanov (North
Carolina), L.Bogatchev(Leeds), A.Ramirez<BR>(Santiago)<BR></FONT></FONT><FONT
face=Arial size=2>Limit theorems in probability are often seen (in particular by
analysts) as tools to get rid of randomness. The Law of Large Numbers, the
Central limit theorem (and its close cousin Homogenization theory) are
such efficient tools to replace complex random media by simple effective
deterministic ones. We will here survey situations of dynamics in random media
where the randomness is irreducible to a deterministic picture, where the
picture in the averaged (or homogenised) medium is very different from the
behaviour in the "quenched" medium (where randomness is frozen), due to the
strong influence of the extreme values of the random elements of the
models.<BR>These examples include Random Walks in Random Traps (or, for
analysts, the heat equation in a randomly perforated domain), branching random
walks in random media (or Random Reaction Diffusion Equations) and if time
permits, dynamics of spin glasses.<BR>We will exhibit that there exists a new
and general rich transition between these two extreme descriptions of the
medium(averaged and quenched). This transition (in its simplest version) can be
seen as a way to interpolate between the two most classical sets of limit
theorems in probability, those for sums of i.i.d random variables, and those for
their extreme values.<BR><BR>Cordiali saluti</FONT></DIV>
<DIV><FONT face=Arial size=2>Segreteria della Classe di
Scienze</FONT></DIV></BODY></HTML>