Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices
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We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as √t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments.
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