A solution of the Gross-Witten matrix model by nonlinear random processes

We illustrate the stochastic method for solving the Schwinger‐Dyson equations in large‐N quantum field theories described in ArXiv:1009.4033 on the example of the Gross‐Witten unitary matrix model. In the strong‐coupling limit, this method can be applied directly, while in the weak‐coupling limit we change the variables from compact to noncompact ones in order to cast the Schwinger‐Dyson equations in the stochastic form. This leads to a new action with an infinite number of higher‐order interaction terms. Nevertheless, such an action can be efficiently handled. This suggests the way to apply the method of ArXiv:1009.4033 to field theories with U(N) field variables as well as to effective field theories in the large‐N limit.