I'm kind of surprised that I've been unable to find a closed form for the expected number of intersections of $n$ independent standard Brownian motions up to time $t > 0$. I'm well aware of the Karlin-McGregor formula which gives the asymptotics of non-intersecting Brownian motions as $t\to\infty$. I have been looking mostly at the literature for coalescing Brownian motions, but the asymptotics are not very precise. Any suggestions?
2026-04-01 00:12:18.1775002338
expected number of of intersections of independent brownian motions on the line
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