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<DIV><FONT face=Arial size=2>alla Scuola Normale si terrà il seguente seminario
di matematica nell'ambito del Colloquio De Giorgi:
<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 size=+0><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></FONT></DIV></FONT></DIV></BODY></HTML>