Random walks are determined by their trace on the positive half-line
Abstract
We prove that the law of a random walk Xn is determined by the one-dimensional distributions of (Xn, 0) for n = 1, 2, …, as conjectured recently by Lo\"ic Chaumont and Ron Doney. Equivalently, the law of Xn is determined by its upward space-time Wiener-Hopf factor. Our methods are complex-analytic.
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