In this paper, along the spirit of Greene, Nijenhuis and Wilf's probabilistic method for the classical hook-length formula for standard Young tableaux, we present a probabilistic proof of the hook-length formula for standard immaculate tableaux, which arose in the study of non-commutative symmetric functions.
"A probabilistic method for the number of standard immaculate tableaux." Rocky Mountain J. Math. 48 (6) 2087 - 2097, 2018. https://doi.org/10.1216/RMJ-2018-48-6-2087