Topics in Products of Random Matrices
Mukherjea, Arunava
Topics in Products of Random Matrices / Arunava Mukherjea - New Delhi : Narosa Pub. House : International distribution by American Mathematical Society, ©2000. - 121p : illustrations ; 24 cm.
1. Introduction --
2. Convergence in Distribution: Products of Random Stochastic Matrices --
3. Nature of the Limit Distribution --
4. Convergence in Direction --
5. Stochastic Flows on a Countable Set: Products of Infinite-dimensional Random Stochastic Matrices --
6. Products of Random Infinite-dimensional Non-negative Matrices: The Equation [actual symbol not reproducible] --
7. Probability Measures on 2 x 2 Stochastic Matrices and a Functional Equation --
8. The Limit Distribution for Products of 2 x 2 Random Stochastic Matrices: A Specific Example --
Appendix: The Multivariate Central Limit Theorem: An Elementary Proof Using a Theorem of P. Chernoff.
These lecture notes contain detailed results on convergence in distribution for products of independent and identically distributed random matrices and also for their normalised versions. Conditions for the limit distribution to be absolutely continuous or continuous singular are discussed and the limit distributions have also been computed for various specific examples. Infinite dimensional matrices are also considered, with reference to random motions of particles." "Semigroup methods have been highlighted throughout the notes. Care has been taken to make the presentation readily accessible to graduate students and beginners in research. Most of the results presented in the notes have not previously appeared in book form."--Jacket
9788173192975
Technical Bureau India Pvt. Ltd. :E/261, Shastri Nagar Delhi
Mathematics
Analysis
Random matrices.
Stochastische Matrix
Functional Equations
515.55 MUK
Topics in Products of Random Matrices / Arunava Mukherjea - New Delhi : Narosa Pub. House : International distribution by American Mathematical Society, ©2000. - 121p : illustrations ; 24 cm.
1. Introduction --
2. Convergence in Distribution: Products of Random Stochastic Matrices --
3. Nature of the Limit Distribution --
4. Convergence in Direction --
5. Stochastic Flows on a Countable Set: Products of Infinite-dimensional Random Stochastic Matrices --
6. Products of Random Infinite-dimensional Non-negative Matrices: The Equation [actual symbol not reproducible] --
7. Probability Measures on 2 x 2 Stochastic Matrices and a Functional Equation --
8. The Limit Distribution for Products of 2 x 2 Random Stochastic Matrices: A Specific Example --
Appendix: The Multivariate Central Limit Theorem: An Elementary Proof Using a Theorem of P. Chernoff.
These lecture notes contain detailed results on convergence in distribution for products of independent and identically distributed random matrices and also for their normalised versions. Conditions for the limit distribution to be absolutely continuous or continuous singular are discussed and the limit distributions have also been computed for various specific examples. Infinite dimensional matrices are also considered, with reference to random motions of particles." "Semigroup methods have been highlighted throughout the notes. Care has been taken to make the presentation readily accessible to graduate students and beginners in research. Most of the results presented in the notes have not previously appeared in book form."--Jacket
9788173192975
Technical Bureau India Pvt. Ltd. :E/261, Shastri Nagar Delhi
Mathematics
Analysis
Random matrices.
Stochastische Matrix
Functional Equations
515.55 MUK
