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Seminários do IMPA

In this seminar, we discuss the Ruelle Operator associated with a random potential  derived from Brownian Motion paths. We associate a main eigenvalue for almost all path of the Brownian Motion and we study the properties of the random variable $\lambda_B$ given by this procedure. Subsequently we construct an useful isometry of a subspace of the Skohorod Space that we use to extract an functional stochastic equation for $\lambda_B$. Finally, we deduce upper and lower bounds for the expectation of $\lambda_B$ according to the Wiener Measure and prove the finiteness of quenched pressure associated with this random potential.