Limit Profiles for Separation Distance

Peter E. Francis; Evita Nestoridi

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arXiv · 2605.19084

Limit Profiles for Separation Distance

Peter E. Francis·Evita Nestoridi

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Abstract

This paper studies limit profiles for the separation distance. A limit profile records the limiting shape of the distance to stationarity inside the cutoff window, at times of the form $t_n+cw_n$. We start with two famous card shuffles, a general setup for inverse riffle shuffles and random transpositions, and we determine their separation distance limit profiles. We then develop a spectral comparison technique and study continuity properties in the style of [Nes24; Nes25], adapted to separation distance. The comparison method is illustrated through random transpositions, as well as random walks on product groups and the hypercube.

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Peter E. Francis, Evita Nestoridi. 2026-05-18. Limit Profiles for Separation Distance. https://arxiv.org/abs/2605.19084

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