Abstract: I will demonstrate that $P(L(t)<1) ~ t^{-(1-H)}$, where $L$ is
the local time at $0$ of any recurrent $H$-self-similar real-valued
process $X$ with stationary increments that admits a sufficiently
regular local time. A special case is the Gaussian setting, i.e. when
the underlying process is fractional Brownian motion, in which the
result settles a conjecture by Molchan [Commun. Math. Phys. 205, 97-111
(1999)] who obtained the upper bound $1-H$ on the exponent.