Vicious Walkers and Random Contraction Matrices
نویسنده
چکیده
The ensemble CUE(q) of truncated random unitary matrices is a deformation of the usual Circular Unitary Ensemble depending on a discrete non-negative parameter q. CUE(q) is an exactly solved model of random contraction matrices originally introduced in the context of scattering theory. In this article, we exhibit a connection between CUE(q) and Fisher’s randomturns vicious walker model from statistical mechanics. In particular, we show that the moment generating function of the trace of a random matrix from CUE(q) is a generating series for the partition function of Fisher’s model, when the walkers are assumed to represent mutually attracting particles.
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