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Lyapunov Exponents for Infinite Dimensional Random Dynamical Systems in a Banach Space
Random Dynamical Systems Lyapunov Exponents
2015/4/3
Metric Dynamical System
Let be a probability space.
Let be a metric dynamical system:
(i)
(ii)
(iii) preserves th...
Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
Spectra of Random Hermitian Matrices Small-Rank External Source
2010/11/24
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, whi...
Number variance for hierarchical random walks and related fluctuations
hierarchical random walks related fluctuations
2010/11/24
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance pr...
Asymmetric directed polymers in random environments
Directed polymers in random environment Directed polymers in Brownian environments
2010/12/14
The model of Brownian Percolation has been introduced as an approx-imation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuati...
Toy Model for Large Non-Symmetric Random Matrices
Singular Values Rectangular Random Matrices Free Random Matrix Theory Vector Models
2010/4/28
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large d...
Estimating generalised Lyapunov exponents for products of random matrices
random matrices large-deviation regime fluid flows
2010/4/7
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorit...
Some Random Fixed Point Theorems for Non-Self Nonexpansive Random Operators
Random fixed point non-self mappings Nonexpansive random operator inwardness condition
2010/2/26
Let (W, S) be a measurable space, with \sum a sigma-algebra of subsets of W, and let E be a nonempty bounded closed convex and separable subset of a Banach space X, whose characteristic of noncompact ...
A popular account of the connection between random walks and electric networks.