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SUMMARY:Probabilities of rare events in product kernel aggregation: exact 
 formula and phase diagram
DTSTART:20260922T080000Z
DTEND:20260922T090000Z
DTSTAMP:20260929T071700Z
UID:indico-event-1926@indico.dfa.unipd.it
DESCRIPTION:Speakers: Goutham R. (The Institute of Mathematical Sciences\,
  Chennai\, India)\n\nWe present an exact method for calculating the large 
 deviation function describing rare fluctuations in the number of particle
 s for product-kernel aggregation. Starting from the master equation\, we
  derive an exact integral representation for the probability $P(M\,N\,t)$
  of observing $N$ particles at time $t$ starting from $M$ monomers for a
 ny  finite $M\, N\, t$. From this\, we obtain an exact expression for th
 e exponential moment $\\langle p^N\\rangle$ for integer $p$. Employing a 
 replica conjecture---numerically validated by finite-$M$ scaling---we ext
 end this result to real $p \\geq 0$. The convex envelope of the large dev
 iation function\, obtained via a Legendre-Fenchel transform of the expone
 ntial moment\, shows singular behavior. The singular structure allows us 
 to construct the full phase diagram of product-kernel aggregation\, which
  contains a tricritical point\, separating continuous and discontinuous t
 ransitions.  We also compute the asymptotic form of the LDF for small $N
 /M$.\n\nhttps://indico.dfa.unipd.it/event/1926/
LOCATION:P1A (Dipartimento di Fisica e Astronomia - Edificio Ricci-Curbast
 ro (ex-Paolotti))
URL:https://indico.dfa.unipd.it/event/1926/
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