The Fundamentals of Heavy Tails

Jayakrishnan Nair is Associate Professor in Electrical Engineering at IIT Bombay. His research focuses on modeling, performance evaluation, and design issues in online learning environments, communication networks, queueing systems, and smart power grids. He is the recipient of best paper awards at IFIP Performance (2010 and 2020) and ACM e-Energy (2020). Adam Wierman is Professor of Computing and Mathematical Sciences at the California Institute of Technology (Caltech). His research develops tools in machine learning, optimization, control, and economics with the goal of making the networked systems that govern our world sustainable and resilient. He is best known for his work spearheading the design of algorithms for sustainable data centers and he is the recipient of numerous awards including the ACM Sigmetrics Rising Star award, the ACM Sigmetrics Test of Time award, the IEEE Communication Society William Bennet Prize, and multiple teaching and best paper awards. Bert Zwart is group leader at CWI Amsterdam and Professor of Mathematics at Eindhoven University of Technology. He has expertise in stochastic operations research, queueing theory, and large deviations, and in the context of heavy tails, he has focused on sample path properties, designing Monte Carlo methods and applications to computer-communication and energy networks. He was area editor of Operations Research, the flagship journal of his profession, from 2009 to 2017, and was the recipient of the INFORMS Applied Probability Society Erlang prize, awarded every two years to an outstanding young applied probabilist.

• Commonly used notation; 1. Introduction; Part I. Properties: 2. Scale invariance, power laws, and regular variation; 3. Catastrophes, conspiracies, and subexponential distributions; 4. Residual lives, hazard rates, and long tails; Part II. Emergence: 5. Additive processes; 6. Multiplicative processes; 7. Extremal processes; Part III. Estimation: 8. Estimating power-law distributions: Listen to the body; 9. Estimating power-law tails: Let the tail do the talking; References; Index.

'Heavy tailed distributions are ubiquitous in many disciplines which use probabilistic models. The book by Nair, Wierman and Zwart is a superb introduction to the topic and presents fundamental principles in a rigorous yet accessible manner. It is a must-read for researchers interested in understanding heavy tails.' R. Srikant, University of Illinois at Urbana-Champaign