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Suppose that $a_1,\dots,a_n,b_1,\dots,b_n$ are iid random variables each with a symmetric non-atomic distribution. Let $p$ denote the probability that there is some real $t$ such that $t a_i \ge b_i$ ...

If I pick a random regular graph on $n$-vertices and degree $d$ from uniform distribution what is the probability that its automorphism group is of size at least $m$? -- I want to know what is the ...