Event time:

Thursday, January 24, 2019 - 4:00pm

Location:

DL 431

Speaker:

Abigail Raz

Speaker affiliation:

Rutgers University

Event description:

Let $X_H$ denote the number of copies of a fixed graph $H$ in the random graph $G(n,p)$. Determining the behavior of $X_H$ has long been a central problem in probabilistic combinatorics. Although many results have been established for this random variable, the problem of determining the upper tail of $X_H$ is still an area of active research. In this talk, we examine the case where $H$ is an $l$-cycle, showing that

$\mathbb{P}(X_H > (1+\epsilon)E[X_H])<\exp[-C_{\epsilon,l}\min\{n^2p^2 \log(1/p),n^lp^l\}]$.

$\mathbb{P}(X_H > (1+\epsilon)E[X_H])<\exp[-C_{\epsilon,l}\min\{n^2p^2 \log(1/p),n^lp^l\}]$.

Research Area(s):