Random Fibonacci Words

Join a comprehensive lecture by Leonid Petrov from the University of Virginia as he explores "Random Fibonacci Words" as part of Harvard CMSA's program on Classical, quantum, and probabilistic integrable systems. Discover how Fibonacci words—sequences of 1's and 2's graded by the total sum of digits—form a differential poset YF that relates to the Young lattice used in symmetric group representations. Learn about "coherent" measures on YF derived from clone Schur functions, understand the parameters that ensure measure positivity, and examine the large-scale behavior of random Fibonacci word ensembles. Explore connections to tridiagonal matrix total positivity, Stieltjes moment sequences, orthogonal polynomials from the (q-)Askey scheme, and residual allocation models. This 71-minute talk presents joint research with Jeanne Scott, offering insights into this fascinating intersection of combinatorics and probability theory.