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Full Description
This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events.
It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus.
Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).
Contents
1. LDP Problems in Quantum Field Theory 2. LDP in Biology, Neural Networks, Electromagnetic Measurements, Cosmic Expansion 3. LDP in Signal Processing, Communication and Antenna Design 4. LDP Applied to Quantum Measurement, Classical Markov Chains, Quantum Stochastics and Quantum Transition Probabilities 5. LDP in Classical Stochastic Process Theory and Quantum Mechanical Transitions 6. LDP in Pattern Recognition and Fermionic Quantum Filtering 7. LDP in Spin Field Theory, Anharmonic Perturbations of Quantum Oscillators, Small Perturbations of Quantum Gibbs States 8. LDP for Electromagnetic Control of Gravitational Waves, Randomly Perturbed Quantum Fields, Hartree-Fock Approximation, Renewal Processes in Quantum Mechanics 9. LDP in Electromagnetic Scattering and String Theory, Control of Dynamical Systems Using LDP 10. LDP in Markov Chain and Queueing Theory with Quantum Mechanical Applications 11. LDP in Device Physics, Quantum Scattering Amplitudes, Quantum Filtering and Quantum Antennas 12. How the Electron Acquires Its Mass, Estimating the Electron Spin and the Quantum Electromagnetic Field Within a Cavity in the Presence of Quantum Noise 13. Mathematical Tools for Large Deviations, Neural Networks, LDP in Physical Theories, EM and LDP Algorithms in Quantum Parameter Estimation and Filtering 14. Quantum Transmission Lines, Engineering Applications of Stochastic Processes 15. More Tools in Probability, Electron Mass in the Presence of Gravity
and Electromagnetic Radiation, More on LDP in Quantum Field Theory, Non-Abelian Gauge Field Theory and Gravitation 16. Weak Convergence, Sanov's Theorem, LDP in Binary Signal Detection 17. LDP for Classical and Quantum Transmission Lines, String Theoretic Corrections to Classical Field Lagrangians, Non-Abelian Gauge Theory in the Language of Differential Forms 18. LDP and EM Algorithm, LDP for Parameter Estimates in Linear Dynamical Systems, Philosophical Questions in Quantum General Relativity
