On the asymptotic equidistribution of word values in symmetric groups

2025/07/18 by Alekseev, Vadim, Schneider, Jakob, Thom, Andreas
#20B30 #20F69 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2507.13928

Abstract

We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution results for values of d-tuples of elements of \mathbb F_d.

Citations

• Free groups are L²-subgroup rigid
• Word maps with constants on symmetric groups
• Girth, words and diameter
• Words, Hausdorff dimension and randomly free groups
• On the Distribution of Values of Certain Word Maps
• Criteria for equidistribution of solutions of word equations on SL(2)
• L²-Homology for von Neumann Algebras
• Word maps have large image

Related

• On the expected number of commutations in reduced words
• Criteria for equidistribution of solutions of word equations on SL(2)
• Central Limit Theorem on the Conjugacy Measure of Symmetric Groups
• Word maps with constants on symmetric groups
• Further equidistribution of set-valued statistics on permutations