Reciprocal Time Relation of Noncolliding Brownian Motion with Drift

Abstract

We consider an $N$-particle system of noncolliding Brownian motion starting from $x_1\le x_2\le ...\le x_N$ with drift coefficients ${\nu }_j,1\le j\le N$ satisfying ${\nu }_1\le {\nu }_2\le ...\le {\nu }_N$. When all of the initial points are degenerated to be zero, $x_j=0,1\le j\le N$, the equivalence is proved between a dilatation with factor $1/t$ of this drifted process and the noncolliding Brownian motion starting from ${\nu }_1\le {\nu }_2\le ...\le {\nu }_N$ 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.

v2: AMS_LaTeX, 17 pages, no figure, minor corrections made for publication in J. Stat. Phys

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• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Exact distribution of the maximal height of p vicious walkers
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Cited by in corpus (2)

• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• System of Complex Brownian Motions Associated with the O'Connell Process