A PDE for non-intersecting Brownian motions and applications
- Adler, Mark
- Delépine, Jonathan
- van Moerbeke, Pierre
- Vanhaecke, Pol
DOIAbstract
AbstractConsider N=n1+n2+⋯+np non-intersecting Brownian motions on the real line, starting from the origin at t=0, with ni particles forced to reach p distinct target points βi at time t=1, with β1<β2<⋯<βp. This can be viewed as a diffusion process in a sector of RN. This work shows that the transition probability, that is the probability for the particles to pass through windows E˜k at times tk, satisfies, in a new set of variables, a non-linear PDE which can be expressed as a near-Wronskian; that is a determinant of a matrix of size p+1, with each row being a derivative of the previous, except for the last column. It is an interesting open question to understand those equations from a more probabilistic point of view.As an application of ...
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