Stochastic Methods in Scientific Computing: From Foundations to Advanced Techniques (Hardcover)

Introduction. Random numbers and probability distribution. Central limit theorem. Beyond the Normal distribution. Exercises. Random walks. Random walk as a Markov process. Random walks in 1 and 2 dimensions. Levy flight. Random walks with potentials. Exercises. Monte Carlo methods. Objectives and concepts. Monte-Carlo integration. Statistical models. Introduction to Statistical Mechanics. The 2D Ising model. The 3-state Potts model in 3D: Finite size scaling. Gauge theories as statistical systems. Advanced MC simulation techniques. Langevin simulations. Hybrid Monte-Carlo simulations. Non-local Monte-Carlo update. Multicanonical simulations. Micro-canonical simulations. Density-of-States techniques. Exercises and computer experiments. From Statistical Systems to Quantum Field Theory. The O(2) model. SU(2) Yang-Mills theory. SU(N) gauge theories. Current challenges in Monte-Carlo Simulations. Sign- and overlap problems. Theories with sign problems. Topological modes and ergodicity problems. Appendix: High-Performance Computing