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VERSION:2.0
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CALSCALE:GREGORIAN
X-WR-CALNAME:Richard P. Stanley Seminar in Combinatorics
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20261009T144244Z
UID:tag:localist.com\,2008:EventInstance_49295765189356
DTSTART:20250410T200000Z
DTEND:20250410T210000Z
DESCRIPTION:Speaker: Matthew Jenssen (King's College London​​​​​
 ​​)\n\nTitle: Non-existence probabilities and lower tails via Gibbs un
 iqueness on hypertrees\n\nAbstract:  \n\nGiven a graph $H$\, what is the p
 robability that $G(n\,p)$ contains no copy of $H$ or fewer copies than exp
 ected? This is a canonical example of a `lower-tail' large deviation proba
 bility that arises naturally in combinatorics. Other examples include the 
 probability that a random subset of $[n]$ avoids $k$-term arithmetic progr
 essions or that a random subset of an abelian group is sum free.  \n \nIn 
 this talk\, I will discuss a method for determining the logarithmic asympt
 otics (or rate function) for such probabilities. The method applies for a 
 range of parameters in the `critical regime': between the regime amenable 
 to hypergraph container methods and that amenable to Janson's inequality. 
  \n \nThe method works in the general framework of estimating the probabil
 ity that a $p$-random subset of vertices of a $k$-uniform hypergraph conta
 ins fewer hyperedges than expected.  We show that under some simple struct
 ural conditions on the hypergraph and an upper bound on $p$ determined by 
 a phase transition on an infinite hypertree\, this probability can be appr
 oximated by a formula derived from a Gibbs measure on the hypertree.\n \n 
 This is joint work with Will Perkins\, Aditya Potukuchi and Michael Simkin
 .
GEO:42.358262;-71.090045
LOCATION:Building 2\, Room 139
SUMMARY:Richard P. Stanley Seminar in Combinatorics
URL;VALUE=URI:https://calendar.mit.edu/event/richard-p-stanley-seminar-in-c
 ombinatorics-5146
CATEGORIES:Conferences/Seminars/Lectures
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