Speaker
Pravabati Chingangbam
(IIA)
Description
Random fields arise in many areas of science, from materials and biology to climate and cosmology. While traditional statistics describe their local properties, topology reveals their global structure. We develop a statistical framework for Betti numbers and the Euler characteristic of excursion sets of smooth random fields by expressing them in terms of random topological components. This representation enables the study of their statistical distributions and Gaussian limits, providing insight into the use of topological statistics for physical inference, particularly in cosmology.