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In this paper we introduce and study a certain intricate Cantor-like set $C$contained in unit interval. Our main result is to show that the set $C$ itself,as well as the set of dissipative points within $C$, both have Hausdorffdimension equal to 1. The proof uses the transience of a certain non-symmetricCauchy-type random walk.

The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics