Department of Mathematics

 Spring 2018

We will meet on Tuesdays at 4:00 pm.
Here is a tentative list of speakers (to be extended): Yevgeniy Kovchegov, Bruno Barbosa
Registration information: Mth 607, Sec 003 - CRN 53504



Title and abstract

Tuesday, May 22, 4:00 pm
WNGR 201
Yevgeniy Kovchegov
Oregon State University

"Tokunaga self-similarity arises naturally from time invariance"

Abstract. The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching processes G(s) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G(s) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G(s) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduce the latter for a particular parameter value.

This is a joint work with Ilya Zaliapin (University of Nevada, Reno).

Past probability seminars: Fall 2005, Winter 2006, Spring 2006, Fall 2006, Winter 2007, Spring 2007, Fall 2007, Winter 2008, Spring 2008, Fall 2008, Winter 2009, Spring 2009, Fall 2009, Winter 2010, Spring 2010, Fall 2010, Winter 2011, Spring 2011, Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017, Spring 2017, Fall 2017, Winter 2018