Explore a 24-minute lecture on the Law of Fractional Logarithms for Extrema of Airy Processes, delivered at the International Centre for Theoretical Sciences as part of a comprehensive program on discrete integrable systems. Delve into advanced mathematical concepts connecting integrable systems, probability theory, and statistical physics. Learn about the intersection of continuous and discrete systems, their solvability properties, and conserved quantities through the lens of Airy processes. Gain insights into how these mathematical structures relate to various branches of theoretical physics and mathematics, including statistical physics, string theory, combinatorics, representation theory, geometry, and probability. Part of a broader two-week program featuring mini-courses, workshops, and problem sessions, focusing on integrable difference equations, cluster algebra structures, and integrable probability.