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New Math Paper Defines Spectral-Gap Constant Bounds

By PulseAugur Editorial · [1 sources] ·

Researchers have established bounds for the optimal normalized spectral-gap constant in sliding-window occupation count kernels. The study proves that for an m-state space, this constant is between 1/(1080m) and q_{m-2}, where q_{r+1}=q_r(1-q_r). This implies the constant is Theta(m^{-1}), meaning the reciprocal optimal comparison cost is linear in m. The paper details a proof combining several advanced mathematical techniques, including decorrelation, decomposition, and inequality estimates, to construct witnesses that approach the derived bounds. AI

RANK_REASON Academic paper published on arXiv detailing mathematical theory. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv stat.ML →

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New Math Paper Defines Spectral-Gap Constant Bounds

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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Yanjin Xiang, Zhihua Zhang ·

    Poincar\'e's Inequality on Sliding-Window Occupation Count Kernels and the Optimal Normalized Spectral-Gap Constant

    arXiv:2609.27836v2 Announce Type: replace-cross Abstract: Let $P$ be an irreducible reversible Markov kernel on an $m$-state space $\Omega$, and denote its right spectral gap by $\Gap(P) =1-\lambda_2(P)$. From a stationary trajectory, let $K_t$ be the occupation-count vector of t…

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