Free Diffusions , Free
نویسنده
چکیده
Motivated by the stochastic quantization approach to large N matrix models, we study solutions to free stochastic diierential equations dX t = dS t ? 1 2 f(X t)dt where S t is a free brownian motion. We show existence, uniqueness and Markov property of solutions. We deene a relative free entropy as well as a relative free Fisher information, and show that these quantities behave as in the classical case. Finally we show that, in contrast with classical diiusions, in general the asymptotic distribution of the free diiusion does not converge, as t ! 1, towards the master eld (i.e. the Gibbs state).
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