Non-intersecting Brownian motions leaving from and going to several points

Details Non-intersecting Brownian motions leaving from and going to several points Non-intersecting Brownian motions leaving from and going to several points

2010-05-07

arxiv.org/abs/1005.1303v2

Mathematics

Probability

36 pages, 1 figure; References added, Revised argument in section 4, results unchanged

Scientific paper

Consider n non-intersecting Brownian motions on $\mathbb{R}$, depending on time $t \in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\leq i\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$, $1\leq j\leq p$. For arbitrary $p$ and $q$, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time $0

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