BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//132.216.98.100//NONSGML kigkonsult.se iCalcreator 2.20.4//
BEGIN:VEVENT
UID:20250811T012353EDT-9405ik5Dh1@132.216.98.100
DTSTAMP:20250811T052353Z
DESCRIPTION:The Strange Logic of Galton-Watson Trees\n\nThis talk will focu
 s on probabilities of first order (FO) and existential monadic second orde
 r (EMSO) sentences on the Galton-Watson (GW) tree. I shall limit myself to
  Poisson offspring distributions\, though many of the results can be exten
 ded to very general distributions. Fix $k in mathbb{N}$. Conditioned on su
 rvival of the tree\, we show that all FO sentences of quantifier depth k a
 re determined by a local neighbourhood of the root (of radius $approx 3^{k
 +2}$). We devise a recursive procedure to compute these probabilities\, co
 nditioned on the tree's survival. The probabilities are very nice function
 s of $lambda$ and $p_{lambda}$\, the survival probability. Using Ehrenfeuc
 ht games and corresponding equivalence classes\, we show that the probabil
 ity of any FO sentence is analytic in $lambda$.\n	\n	I shall discuss some of
  our ongoing work: rogue solutions\, i.e. solutions of equations derived f
 rom tree automata that do not admit any interpretation\; an example of a s
 entence that is not expressible almost surely as an EMSO\, etc. I shall en
 d with speculations and conjectures that hopefully the audience will find 
 fascinating.\n
DTSTART:20170126T213000Z
DTEND:20170126T223000Z
LOCATION:room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Moumanti Podder\, Courant Institute
URL:/mathstat/channels/event/moumanti-podder-courant-i
 nstitute-265231
END:VEVENT
END:VCALENDAR