Theoretical Statistics and Mathematics Unit, ISI Delhi

July 17, 2019 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Debleena Thacker,
Department of Mathematics, Uppsala University, Sweden

Title:
Embedding balanced infinite color urn models into trees

Abstract of Talk

In this work the authors introduce the embedding into \emph{random recursive trees} to study classical and generalized balanced urn models with non-negative balanced replacement matrices, for both finite and infinitely many colors. We provide a coupling of the balanced urn model with \textit{branching Markov chain on a random recursive tree}, and use the properties of the later to deduce results for the former. We use this embedding to calculate the covariance between the proportions of any two colors when the replacement matrix is irreducible, aperiodic, positive recurrent and uniformly ergodic. This proves the strong law of large numbers for the proportion of colors. This method is especially useful for infinitely many colors, since the use of operator theory leads to technical difficulties for infinitely many colors.

Based on joint works with Antar Bandyopadhyay and Svante Janson