Abstract
This is an introduction to the theory of onedimensional disordered systems and products of random matrices, confined to the 2 by 2 case. The notion of impurity model that is, a system in which the interactions are highly localised links the two themes and enables their study by elementary mathematical tools.
After discussing the spectral theory of some impurity models, we state and illustrate Furstenberg's theorem, which gives sufficient conditions for the exponential growth of a product of independent, identicallydistributed matrices.
After discussing the spectral theory of some impurity models, we state and illustrate Furstenberg's theorem, which gives sufficient conditions for the exponential growth of a product of independent, identicallydistributed matrices.
Original language  English 

Title of host publication  Stochastic Processes and Random Matrices 
Subtitle of host publication  Lecture Notes of the Les Houches Summer School 2015 
Editors  Gregory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, Leticia F. Cugliandolo 
Place of Publication  Oxford 
Publisher  Oxford University Press 
Chapter  11 
Number of pages  71 
Volume  104 
ISBN (Print)  9780198797319 
DOIs  
Publication status  Published  10 Aug 2017 
Publication series
Name  Lecture Notes of the Les Houches Summer School 

Publisher  OUP 
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Dr Yves J M Tourigny
 Probability, Analysis and Dynamics
 School of Mathematics  Senior Lecturer in Numerical Analysis
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member