TY - BOOK
T1 - Stochastic processes and random matrices
T2 - Lecture notes of the Les Houches summer school
AU - Schehr, GrĂ©gory
AU - Altland, Alexander
AU - Fyodorov, Yan V.
AU - O'Connell, Neil
AU - Cugliandolo, Leticia F.
PY - 2018/1/18
Y1 - 2018/1/18
N2 - The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).
AB - The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).
UR - http://www.scopus.com/inward/record.url?scp=85052640972&partnerID=8YFLogxK
U2 - 10.1093/oso/9780198797319
DO - 10.1093/oso/9780198797319
M3 - Book
AN - SCOPUS:85052640972
SN - 9780198797319
VL - 104
BT - Stochastic processes and random matrices
PB - Oxford University Press
ER -
TY - CHAP
T1 - Random Matrix Theory of resonances
T2 - 2016 URSI International Symposium on Electromagnetic Theory, EMTS 2016
AU - Fyodorov, Yan V.
PY - 2016/9/19
Y1 - 2016/9/19
N2 - Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated eigenfunctions remains one of the pillars of theoretical understanding of quantum chaotic systems. In a scattering system coupling to continuum via antennae converts real eigenfrequencies into poles of the scattering matrix in the complex frequency plane and the associated eigenfunctions into decaying resonance states. Understanding statistics of these poles, as well as associated non-orthogonal resonance eigenfunctions within RMT approach is still possible, though much more challenging task.
AB - Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated eigenfunctions remains one of the pillars of theoretical understanding of quantum chaotic systems. In a scattering system coupling to continuum via antennae converts real eigenfrequencies into poles of the scattering matrix in the complex frequency plane and the associated eigenfunctions into decaying resonance states. Understanding statistics of these poles, as well as associated non-orthogonal resonance eigenfunctions within RMT approach is still possible, though much more challenging task.
UR - http://www.scopus.com/inward/record.url?scp=84992128522&partnerID=8YFLogxK
U2 - 10.1109/URSI-EMTS.2016.7571486
DO - 10.1109/URSI-EMTS.2016.7571486
M3 - Other chapter contribution
AN - SCOPUS:84992128522
SP - 666
EP - 669
BT - 2016 URSI International Symposium on Electromagnetic Theory, EMTS 2016
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 14 August 2016 through 18 August 2016
ER -