Percolation Theory

Percolation models are mathematical models for the flow of fluid in a random medium, in which a random medium is associated with the medium rather than the fluid.  They are relevant to the study of phase transitions and critical phenomena, with applications to spontaneous magnetization, thermal phase transitions, gelation processes, clustering phenomena, and the spread of epidemics.  The medium is represented by a lattice graph, from which edges or vertices are deleted at random.  Considerable interest focuses on the concept of the critical probability, the threshold edge-or-vertex retention probability above which infinite connected components exist in the lattice graph.  My research focuses on finding exact values and accurate bounds for the critical probability of various lattices.
 

Publications

I have published over 70 professional papers and books, mostly on percolation theory and random graphs.  Other topics include partially ordered sets, a Berry-Esseen theorem for U-statistics, epidemic models, and statistical estimation in microbiology.
 

Collaborators

I have co-authored publications with:

Sven Erick Alm
Martin Appel
Michael Beer
Bela Bollobas
Elvan Ceyhan
Y. K. Chan
Rulian Cheng
Jason DeVinney
John Gimbel
Larry Gray
D. Kurtz
Matthew Lad
George Lam
Linda Lesniak
Xue Lin
Tomasz Luczak
William D. May
David J. Marchette
Sajod Moradi
Dora Passen Naor
Krzysztof Nowicki
Robert Parviainen
Boris Pittel
Carey Priebe
Wolfgang Reh
Edward Scheinerman
Robert T. Smythe
C. J. Stoeckert
Muhammad Q. Vahidi-Asl
J. W. Wiggins
Brian Yagoda 

My Erdos Number is 2.  (via Bela Bollobas, Tomasz Luczak, and Boris Pittel)
 

Consulting

I have worked on consulting projects for Baltimore Gas & Electric (quality control statistics), JLG Industries (sales forecasting and data summarization), JHU Engineering School (course evaluation survey design and tabulation), and JHU Enrollment Services (enrollment prediction modeling).