BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Wojciech Samotij (Tel Aviv University) DTSTART:20200611T070000Z DTEND:20200611T080000Z DTSTAMP:20260423T035026Z UID:SCMSComb/2 DESCRIPTION:Title: Large deviations of triangle counts in the binomial random graph I\nb y Wojciech Samotij (Tel Aviv University) as part of SCMS Combinatorics Sem inar\n\n\nAbstract\nSuppose that $Y_1\, \\ldots \, Y_N$ are i.i.d. (indepe ndent identically distributed) random variables and let $X = Y_1 + … + Y _N$. The classical theory of large deviations allows one to accurately est imate the probability of the tail events $X < (1-c)E[X]$ and $X > (1+c)E[X ]$ for any positive $c$. However\, the methods involved strongly rely on t he fact that X is a linear function of the independent variables $Y_1\, …\, Y_N.$ There has been considerable interest—both theoretical and pr actical—in developing tools for estimating such tail probabilities also when $X$ is a nonlinear function of the $Y_i$. One archetypal example stud ied by both the combinatorics and the probability communities is when $X$ is the number of triangles in the binomial random graph $G(n\,p)$.\n\nTalk I: We will give a very gentle introduction to the theory of large deviati ons and discuss the history of the large deviation problem for triangle co unts.\n LOCATION:https://researchseminars.org/talk/SCMSComb/2/ END:VEVENT END:VCALENDAR