ORIE Professors Patie and Samorodnitsky organize “Adventures in Self-Similarity”

Nearly two dozen scholars from the Canada, China, England, France, India, Israel, Mexico, Poland, Switzerland, Ukraine and the United States shared research results at a conference about the mathematics of a phenomenon that occurs in communication networks, finance, geology, hydrology, and many other disciplines.  

According to ORIE Professor Gennady Samorodnitsky, self-similarity “is found everywhere.”  In the popular view, it is associated with spatial phenomena in the form of fractal geometry, a standard example of which is the shape of coastlines that look similar at smaller and smaller scales as one zooms in.  The conference was devoted to the mathematics of self-similarity occurring in random processes that unfold over time.  For example, the absolute returns of equity data in finance show similar patterns at different time scales, as does Ethernet traffic, as seen at right (presented at ACM SIGComm ´93 by former ORIE professor Murad Taqqu and coauthors). Mathematical models based on the idea of self-similarity can yield valuable insights into the behavior of these and other processes. Although the applications are broad, the recent conference was devoted to expanding the understanding of the mathematics of self-similarity, with talks on such topics as “an isomorphism theorem for infinitely divisible processes” and “sample paths of the solution to the heat equation with fractional noise.” Videos of some of the talks are here. 

Samorodnitsky organized the conference together with ORIE Associate Professor Pierre Patie, Loïc Chaumont of the Université d’Angers and Yimin Xiao of Michigan State University.  The conference was sponsored by ORIE, the Cornell Department of Mathematics, and a program at the Université Libre de Bruxelles with which Patie was previously affiliated.

Among the attendees who delivered papers at the conference were Takashi Owada, PhD ’13 and Parthanil Roy, PhD ’07, both PhD students of Samorodnitsky. Owada is EC Senior Researcher at the Technion-Israel Institute of Technology in Haifa, Israel; Roy is an Assistant Professor at the Indian Statistical Institute in Kolkata, India.  He commented that “the conference was very well-organized with ample time for discussions, academic interactions, etc.  Also for me, it was very very nostalgic to go back to Ithaca and an honour to take part in a conference of this status.” 

Another student of Samordnitsky, Arijit Chakrabarty PhD '10, attended the confrence.  He is an Assistant Professor at the Indian Statistical Institute in Delhi, India.  Bikramjit Das, PhD ’09, currently at the Singapore University of Technology and Design, was visiting  and also attended some conference sessions.  He is a student of ORIE Professor Sidney Resnick.