Appears in collection : 2024 - T3 - Mini-WS - Computational group theory and applications workshop

Let A and B be 2x2 matrices. Let w(A, B) be a word of length n. After evaluating w(A, B) as a product of matrices, we get a 2x2 matrix, call it W. The problems that we consider are: What is the largest (by the absolute value) possible entry of W, over all w(A, B) of length n, as a function of n? What is the expected absolute value of the largest (by the absolute value) entry in a random product of n matrices, where each matrix is A or B with probability 0.5?