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Title List

A Basic Course in Measure and Probability: Theory for Applications by Ross Leadbetter, Stamatis Cambanis, Vladas PipirasISBN: 9781139103947
Publication Date: 2012

Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning by Loïc Chaumont, Marc YorISBN: 9781139135351
Publication Date: 2012

Fractals in Probability and Analysis by Christopher J. Bishop; Yuval PeresISBN: 9781316460238
Publication Date: 20170119
This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, selfsimilar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.
Price : $210

Gaussian Processes on Trees by Anton BovierISBN: 9781316675779
Publication Date: 20161117
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of meanfield spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to meanfield spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the FKPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a selfcontained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.
Price : $210

Mathematics of TwoDimensional Turbulence by Sergei Kuksin; Armen ShirikyanISBN: 9781139137119
Publication Date: 20121005
This book is dedicated to the mathematical study of twodimensional statistical hydrodynamics and turbulence, described by the 2D NavierStokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x)  proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
Price : $135

Noise Sensitivity of Boolean Functions and Percolation by Christophe Garban; Jeffrey E. SteifISBN: 9781139924160
Publication Date: 20141218
This is a graduatelevel introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the nowfamous SchrammLoewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourieranalytic setup, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging.
Price : $210

Normal Approximations with Malliavin Calculus: From Stein's Method to Universality by Ivan Nourdin, Giovanni PeccatiISBN: 9781139084659
Publication Date: 2012

Probability and Statistics by Example by Yuri Suhov, Mark KelbertISBN: 9781139087773
Publication Date: 2014

Probability on Real Lie Algebras by Uwe Franz; Nicolas PrivaultISBN: 9781316415054
Publication Date: 20160205
This monograph is a progressive introduction to noncommutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for noncommutative couples of random variables, noncommutative stochastic processes with independent increments (quantum Lvy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to noncommutativity in stochastic calculus, Lvy processes, and the Malliavin calculus.
Price : $135

Probability on Trees and Networks by Russell Lyons; Yuval PeresISBN: 9781316672815
Publication Date: 20170119
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the masstransport technique, and connections on random walks on graphs to embedding in Hilbert space. This stateoftheart account of probability on networks will be indispensable for graduate students and researchers alike.
Price : $210

Quantum Stochastics by MouHsiung ChangISBN: 9781107706545
Publication Date: 20150205
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, selfcontained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigroups and processes, and largetime asymptotic behavior of quantum Markov semigroups.
Price : $210

Stochastic Analysis by Hiroyuki Matsumoto; Setsuo TaniguchiISBN: 9781316492888
Publication Date: 20161117
Thanks to the driving forces of the It calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduatelevel text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, pathspaceoriented approach, this book crystallizes modern day stochastic analysis into a single volume.
Price : $210

The Surprising Mathematics of Longest Increasing Subsequences by Dan RomikISBN: 9781139872003
Publication Date: 20141005
In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the VershikKerovLoganShepp limit shape theorem, the BaikDeiftJohansson theorem, the TracyWidom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduatelevel audience for the first time in a highly polished presentation.
Price : $210

Understanding Probability by Henk TijmsISBN: 9781139206990
Publication Date: 20120805
Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain MonteCarlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuoustime Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easygoing style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.
Price : $210

Uniform Central Limit Theorems by R. M. DudleyISBN: 9781139014830
Publication Date: 20140605
In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the BretagnolleMassart theorem giving constants in the KomlosMajorTusnady rate of convergence for the classical empirical process, Massart's form of the DvoretzkyKieferWolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform GlivenkoCantelli classes of functions, Gin and Zinn's characterization of uniform Donsker classes, and the BousquetKoltchinskiiPanchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinitedimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.
Price : $210