Knots and random walks in vibrated granular chains

We study experimentally statistical properties of the opening times of knot s in vertically vibrated granular chains. Our measurements are in good qual itative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling f unction which is independent of the chain length, with a corresponding diff usive characteristic time scale. Both the large-exit-time and the small-exi t-time tails of the distribution are suppressed exponentially, and the corr esponding decay coefficients ore in excellent agreement with theoretical va lues.