What does this research mean for the field?

The fluctuations of the position of a new box created during Schensted row insertion into a random tableau are asymptotically Gaussian as the size of the Young diagram approaches infinity, with mean and variance expressed in terms of Kerov's transition measure. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To characterize the asymptotic probabilistic behavior and position fluctuations of a new box created by Schensted row insertion into large random tableaux.

August 30, 2026The Annals of ProbabilityOpen Access

Fluctuations of Schensted row insertion

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Authors

MMMikołaj Marciniak PŚPiotr Śniady

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Overview

Theoretical analysis uncovers asymptotically Gaussian fluctuations during Schensted row insertion in large Young diagrams, indicating predictable limiting behavior in randomized combinatorial...

Key Points

To characterize the asymptotic probabilistic behavior and position fluctuations of a new box created by Schensted row insertion into large random tableaux.
Analyzed the stochastic properties of inserting a deterministic entry into a random tableau of shape λ as diagram size approaches infinity.
Computed the asymptotic mean and variance of box placement fluctuations using Kerov's transition measure.
Formulated theoretical extensions for the Robinson–Schensted–Knuth algorithm applied to sequences of independent, identically distributed random variables.
Demonstrated that fluctuations of the inserted box position around its expectation are asymptotically Gaussian as the Young diagram size tends to infinity.
Derived explicit expressions for the asymptotic mean and variance of box coordinate fluctuations using Kerov's transition measure of the diagram.
Established an explicit conjecture describing limiting distributional behavior when applying the algorithm to long sequences of independent, identically distributed inputs.

Cite This Study

Marciniak et al. (2026) studied this question.

synapsesocial.com/papers/6a93efc06c1a8fb52e79bc89 https://doi.org/10.1214/25-aop1812

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August 30, 2026The Annals of ProbabilityOpen Access

Fluctuations of Schensted row insertion

View Full Paper

Ask AI

Bookmark

Authors

MMMikołaj Marciniak PŚPiotr Śniady

Discussion

Member takes

Overview

Theoretical analysis uncovers asymptotically Gaussian fluctuations during Schensted row insertion in large Young diagrams, indicating predictable limiting behavior in randomized combinatorial...

Key Points

To characterize the asymptotic probabilistic behavior and position fluctuations of a new box created by Schensted row insertion into large random tableaux.
Analyzed the stochastic properties of inserting a deterministic entry into a random tableau of shape λ as diagram size approaches infinity.
Computed the asymptotic mean and variance of box placement fluctuations using Kerov's transition measure.
Formulated theoretical extensions for the Robinson–Schensted–Knuth algorithm applied to sequences of independent, identically distributed random variables.
Demonstrated that fluctuations of the inserted box position around its expectation are asymptotically Gaussian as the Young diagram size tends to infinity.
Derived explicit expressions for the asymptotic mean and variance of box coordinate fluctuations using Kerov's transition measure of the diagram.
Established an explicit conjecture describing limiting distributional behavior when applying the algorithm to long sequences of independent, identically distributed inputs.

Cite This Study

Marciniak et al. (2026) studied this question.

synapsesocial.com/papers/6a93efc06c1a8fb52e79bc89 https://doi.org/10.1214/25-aop1812

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