This book is divided into two parts the first of which seeks to connect the phase transitions
of various disciplines including game theory and to explore the synergies between statistical
physics and combinatorics. Phase Transitions has been an active multidisciplinary field of
research bringing together physicists computer scientists and mathematicians. The main
research theme explores how atomic agents that act locally and microscopically lead to
discontinuous macroscopic changes. Adopting this perspective has proven to be especially useful
in studying the evolution of random and usually complex or large combinatorial objects (like
networks or logic formulas) with respect to discontinuous changes in global parameters like
connectivity satisfiability etc. There is of course an obvious strategic element in the
formation of a transition: the atomic agents selfishly seek to optimize a local parameter.
However up to now this game-theoretic aspect of abrupt locally triggered changes had not been
extensively studied. In turn the book's second part is devoted to mathematical and
computational methods applied to the pricing of financial contracts and the measurement of
financial risks. The tools and techniques used to tackle these problems cover a wide spectrum
of fields like stochastic calculus numerical analysis partial differential equations
statistics and econometrics. Quantitative Finance is a highly active field of research and is
increasingly attracting the interest of academics and practitioners alike. The material
presented addresses a wide variety of new challenges for this audience.
