Reciprocal Time Relation of Noncolliding Brownian Motion with Drift

Details Reciprocal Time Relation of Noncolliding Brownian Motion with Drift Reciprocal Time Relation of Noncolliding Brownian Motion with Drift

2012-04-25

arxiv.org/abs/1204.5629v1

Mathematics

Probability

AMS_LaTeX, 17 pages, no figure

Scientific paper

We consider an $N$-particle system of noncolliding Brownian motion starting from $x_1 \leq x_2 \leq ... \leq x_N$ with drift coefficients $\nu_j, 1 \leq j \leq N$ satisfying $\nu_1 \leq \nu_2 \leq ... \leq \nu_N$. When all of the initial points are degenerated to be zero, $x_j=0, 1 \leq j \leq N$, the equivalence is proved between a dilatation with factor $1/t$ of this drifted process and the noncolliding Brownian motion starting from $\nu_1 \leq \nu_2 \leq ... \leq \nu_N$ without drift observed at reciprocal time $1/t$, for arbitrary $t > 0$. Using this reciprocal time relation, we study the determinantal property of the noncolliding Brownian motion with drift having finite and infinite numbers of particles.

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