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We study the scaling exponents of a 1+1-dimensional directed polymer in aBrownian random environment introduced by O'Connell and Yor. For a version ofthe model with boundary conditions that are stationary in a space-time sense weidentify the exact values of the exponents. For the version without theboundary conditions we get the conjectured upper bounds on the exponents.

Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment