Symmetry and Convergence

          @misc{ scivideos_22597,
            doi = {},
            url = {https://old.simons.berkeley.edu/node/22597},
            author = {},
            keywords = {},
            language = {en},
            title = {Symmetry and Convergence},
            publisher = {The Simons Institute for the Theory of Computing},
            year = {2022},
            month = {sep},
            note = {22597 see, \url{https://scivideos.org/simons-institute/22597}}
          }
          

Abstract

Abstract A random structure exhibits symmetry if its law remains invariant under a group of transformations. Exchangeability (of graphs, sequences, etc) and stationarity are examples. Under suitable conditions, the transformation group can be used to define an estimator that averages over an instance of the structure, and such estimators turn out to satisfy a law of large numbers, a central limit theorem, and further convergence results. Loosely speaking: The large-sample theory of i.i.d averages still holds if the i.i.d assumption is substituted by a suitable symmetry assumption.  Joint work with Morgane Austern.