Adhesive riffle shuffles: one-parameter models and mixing bounds
Abstract
We compare four simple shuffles with one adhesion parameter p: a card-weighted sticky riffle, a block-weighted riffle, a midpoint-interpolation shuffle, and a correlated-label inverse riffle. Independent surviving contacts create contiguous blocks; no force or energy constants are fitted. We give polynomial upper bounds with explicit dependence on p, common adjacency-survival lower bounds, and a sharper information lower bound for interpolation. For fixed deck size n≥4, the mixing time diverges as Θ((1−p)−1) for the three cut-first models, but as Θ((1−p)−2) for the correlated-label model. The latter distinction comes from whether one or two additional contact breaks are needed to escape cyclic rotations. For even n, unglued interpolation retains the lower bound Ω(√nlog n) and upper bound O(n5/2log n). We distinguish proved bounds from conjectured scales, recover classical riffle cutoff under sufficiently small perturbations, and explain precisely where established results on clumpy shuffles apply. The fixed-parameter asymptotic orders of the new cut-first families and their possible cutoff remain unresolved.
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BibTeX
@misc{jiang2026adhesive,
title = {{Adhesive riffle shuffles: one-parameter models and mixing bounds}},
author = {Yunjiang Jiang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02092},
eprint = {2611.02092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02092},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adhesive riffle shuffles: one-parameter models and mixing bounds
AU - Yunjiang Jiang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02092
UR - https://arxiv.org/abs/2611.02092
AB - We compare four simple shuffles with one adhesion parameter p: a card-weighted sticky riffle, a block-weighted riffle, a midpoint-interpolation shuffle, and a correlated-label inverse riffle. Independent surviving contacts create contiguous blocks; no force or energy constants are fitted. We give polynomial upper bounds with explicit dependence on p, common adjacency-survival lower bounds, and a sharper information lower bound for interpolation. For fixed deck size n≥4, the mixing time diverges as Θ((1−p)^−1) for the three cut-first models, but as Θ((1−p)^−2) for the correlated-label model. The latter distinction comes from whether one or two additional contact breaks are needed to escape cyclic rotations. For even n, unglued interpolation retains the lower bound Ω(√nlog n) and upper bound O(n^5/2log n). We distinguish proved bounds from conjectured scales, recover classical riffle cutoff under sufficiently small perturbations, and explain precisely where established results on clumpy shuffles apply. The fixed-parameter asymptotic orders of the new cut-first families and their possible cutoff remain unresolved.
ER -