Limit Profiles for Separation Distance
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909055114543104 |
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| author | Francis, Peter E. Nestoridi, Evita |
| author_facet | Francis, Peter E. Nestoridi, Evita |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19084 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit Profiles for Separation Distance Francis, Peter E. Nestoridi, Evita Probability Combinatorics 60J05, 60J10, 60J25, 60J27, 60J28, 60C05 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. |
| title | Limit Profiles for Separation Distance |
| topic | Probability Combinatorics 60J05, 60J10, 60J25, 60J27, 60J28, 60C05 |
| url | https://arxiv.org/abs/2605.19084 |