Two-state free Brownian motions Institutional Repository Document uri icon

abstract

  • In a two-state free probability space $(A, phi, psi)$, we define an algebraic two-state free Brownian motion to be a process with two-state freely independent increments whose two-state free cumulant generating function is quadratic. Note that a priori, the distribution of the process with respect to the second state $psi$ is arbitrary. We show, however, that if $A$ is a von Neumann algebra, the states $phi, psi$ are normal, and $phi$ is faithful, then there is only a one-parameter family of such processes. Moreover, with the exception of the actual free Brownian motion (corresponding to $phi = psi$), these processes only exist for finite time.

author list (cited authors)

  • Anshelevich, M.

citation count

  • 0

complete list of authors

  • Anshelevich, Michael

Book Title

  • arXiv

publication date

  • June 2010