2025/07/24 by Gabriel Raposo, Raposo, Gabriel
Economics, Econometrics and Finance · Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2507.18601
openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distributions induced by extreme characters of the infinite symmetric group S_∞. In all cases, we identify the limiting fluctuations as a conditioned Gaussian Free Field.