Anti-concentration conjecture for the independence number of sparse random graphs with a fixed number of edges

Let $G_{n,m}$ be the random graph with $n$ vertices and $m$ edges, and let $falpha(G_{n,m})$ denote its independence number. Suppose

$$m=n^{\eta}$$

where $falpha$ is a constant such that $1<falpha<4/3$. Anti-concentration conjecture. Then $falpha(G_{n,m})$ is not concentrated on $n^{2-3falpha/2-\epsilon}$ values. At the moment, no lower bound on the extent of concentration of $falpha(G_{n,m})$ is known in this regime; the conjecture concerns anti-concentration for $m\leq n^{4/3}$.