Intuitive proofs of Ergodic Theorems

Ergodic Theorems are widely used in dynamical systems and Probability Theory.
In this expository lecture, I will present simple proofs of the Birkhoff Pointwise Ergodic Theorem and The Kingman Subadditive Ergodic Theorem following Katznelson-Weiss, Keane and Steele.
I will try to present these proofs in an intuitive way, so that that they can be remembered. I will then describe applications to random walks on groups

Speaker Details

Yuval Peres is a Principal Researcher and manager of the Theory group at Microsoft Research. Before joining MSR in 2006, he was a Professor at UC Berkeley.
He has also taught at Yale and at the Hebrew University. Yuval has published more than 160 papers with 90 co-authors and has mentored 15 PhD theses. His research encompasses most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has recently co-authored books on Markov chains and mixing times, on zeros of Gaussian analytic functions, and on Brownian motion. Yuval is an IMS fellow and a recipient of the Rollo Davidson prize. In 2001 he received the Loeve prize, awarded once every two years to a leading probabilist under the age of 45. In 2002, Yuval was an invited speaker at the International Congress of Mathematicians in Beijing and in 2009, he delivered a plenary talk at SODA. His favorite quote is from his son Alon, who was overheard at age 6 asking a friend: “Leo, do you have a religion? You know, a religion, like Christian, or Jewish, or Mathematics….?”

Series:
Microsoft Research Talks
Date:
Speakers:
Yuval Peres
Affiliation:
Microsoft Research Redmond

    • Portrait of Jeff Running

      Jeff Running

    • Portrait of Yuval Peres

      Yuval Peres

      Principal Researcher

Series: Microsoft Research Talks