"The Department of Mathematics at the University of Illinois has historically had a strong reputation in probability, both through its faculty and through the many postdoctoral visitors who have been here." From Probability, Department of Mathematics, University of Illinois at Urbana-Champaign
"Topics of interest to the faculty at the University of Illinois include martingale theory, interacting particle systems, general theory of Markov processes, random fields, stochastic differential equations, diffusion processes, and limit theorems. A common element of these topics is a triple (w, £, P) consisting of a collection of outcomes w, a class £ of subsets A of which are called events, and a probability function P which assigns to each event A a probability P(A). Each of the topics comes about by specifying a collection (X(t): t in T) of functions, called random variables or vectors, defined on 2 taking on values in some prescribed space and probabilistic statements relating the X." From Graduate Study in Probability Theory, Department of Mathematics, University of Illinois at Urbana-Champaign
Books on probability can be found in the Mathemathics Library Stacks shelved under call number range 519 to 520.
"Probability theory provides the mathematical framework for the study of experiments for which the outcome is unpredictable by virtue of some intrinsic chance mechanism. The ideas and methods that are continually being developed for this provide powerful tools for many other things, for example, the discovery and proof of new theorems in other parts of mathematics." From Graduate Study in Probability Theory, Department of Mathematics, University of Illinois at Urbana-Champaign
"probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance." From "probability." Encyclopaedia Britannica. Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2015. Web. 02 Jun. 2015.