Almost surely, Brownian motion has a unique minimizer on every interval with rational endpoints, by rescaling part (iv). Every local minimum is the minimum on some rational interval contained in a witnessing neighbourhood. Each rational interval contributes at most one point, and there are countably many such intervals. The set of local minima is therefore countable.


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 201 / 2 / a / v / Solution

 Solution (source code)