My foremost acknowledgment is to all of the people who have taught me analysis of Boolean functions, especially Guy Kindler and Elchanan Mossel. I also learned a tremendous amount from my advisor Madhu Sudan, and my coauthors and colleagues Per Austrin, Eric Blais, Nader Bshouty, Ilias Diakonikolas, Irit Dinur, Uri Feige, Ehud Friedgut, Parikshit Gopalan, Venkat Guruswami, Johan Håstad, Gil Kalai, Daniel Kane, Subhash Khot, Adam Klivans, James Lee, Assaf Naor, Joe Neeman, Krzysztof Oleszkiewicz, Yuval Peres, Oded Regev, Mike Saks, Oded Schramm, Rocco Servedio, Amir Shpilka, Jeff Steif, Benny Sudakov, Li-Yang Tan, Avi Wigderson, Karl Wimmer, John Wright, Yi Wu, Yuan Zhou, and many others. Ideas from all of them have strongly informed this book.
Many thanks to my PhD students who suffered from my inattention during the completion of this book: Eric Blais, Yuan Zhou, John Wright, and David Witmer. I’d also like to thank the students who took my 2007 and 2012 courses on analysis of Boolean functions; special thanks to Deepak Bal, Carol Wang, and Patrick Xia for their very helpful course writing projects.
Thanks to my editor Lauren Cowles for her patience and encouragement, to the copyediting team of David Anderson and Rishi Gupta, and to Cambridge University Press for welcoming the free online publication of this book. Thanks to Luca Trevisan and Radu Grigore for an initial version of LaTeX2WP. Thanks also to Amanda Williams for the use of the “Grey cube” logo/cover image.
I’m very grateful to all the heroes who suggested improvements and pointed out mistakes on this blog. Special thanks in this group to Matt Franklin and Li-Yang Tan; extra-special thanks in this group to Noam Lifshitz.
I’m grateful to Denis Thérien for inviting me to lecture at the Barbados Complexity Workshop, to Cynthia Dwork and the STOC 2008 PC for inviting me to give a tutorial, and to the Simons Foundation who arranged for me to co-organize a symposium together with Elchanan Mossel and Krzysztof Oleskiewicz, all on the topic of analysis of Boolean functions. These opportunities greatly helped me to crystallize my thoughts on the topic.
I worked on this book while visiting the Institute for Advanced Study in 2010–2011 (supported by the Von Neumann Fellowship and in part by NSF grants DMS-0835373 and CCF-0832797); I’m very grateful to them for having me and for the wonderful working environment they provided. The remainder of the work on this book was done at Carnegie Mellon; I’m of course very thankful to my colleagues there and to the Department of Computer Science. “Reasonable” random variables were named after the department’s “Reasonable Person Principle”. I was also supported in this book-writing endeavor by the National Science Foundation, specifically grants CCF-0747250 and CCF-1116594. As usual: “This material is based upon work supported by the National Science Foundation under grant numbers listed above. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).”
Finally, I’d like to thank all of my colleagues, friends, and relatives who encouraged me to write and to finish the book, Zeynep most of all.