2 problems

Exponential-moment conjecture. In the supercritical case $alpha>1$, the random variable $(R^*)^d$ has a finite exponential moment; equivalently, there exists $c>0$ such that

Let $n_1<n_2$ tend to infinity with $n_2/n_1\to 1$, and let $S(\bold n)$ denote the number of stable matchings in the random stable matching problem with $n_1$ men and $n_2$ women.…