High Dimensional Random Walks, Mutli-Layer-Samplers, and Applications to Codes

High dimensional random walks on high dimensional expanders are being studied extensively recently and have found various applications. In this talk, I will describe a new object called a Multi-Layer-Sampler that emerges from high dimensional random walks. This notion extends the well studied notion of samplers in a strong sense. I will discuss the usefulness of multi-layer-samplers for robust testing of codes and hint on other applications of this object.