Abstract
This paper deals with the spectrum of an operator associated with a special kind of random walk. The operator is related to the Metropolis algorithm, an important tool of large-scale scientific computing. The spectrum of this operator has both dis-I crete and continuous parts. There is an interesting challenge due to the fact that any finite-dimensional approxirnation has only eigenval ues. Patterns are presented which give an idea of the full spectrum of this operator.
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