Topic: Random Walks

Ramon van Handel surveys recent progress on constructing graphs, manifolds and groups with optimal spectral gaps, which control how rapidly random walks explore a structure. The talk describes a polynomial method that proves optimality in new settings and connects these developments to longstanding questions about the prevalence of optimal gaps.

This study explores the decision-making processes involved in trajectory extrapolation tasks. Vertical paths were disturbed in the horizontal direction by noise generated by Random Walks (RDW) or Independent and Identically Distributed (IID) noise. In the Experiment, participants (n = 28) extrapolated if a moving point would end right or left of the screen’s center. We modeled path extrapolation using a three-parameter Random Sampling Model (RSM), and a Multi-Layer Perceptron (MLP). Statistically, for RDW paths, the optimal extrapolation strategy is to use the last visible position, whereas fo