Christopher Bose

Decay of correlation for random intermittent maps

We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the sharp rate of correlation decay for the map with the fastest relaxation rate.

Generalized baker's transformations

A class of automorphisms of the unit square called generalized bakerstransformations (gbt) is defined in such a way that every stationary stochastic process may be represented as the movement of a simple partition of the square under a gbt. This extends the classical example of the representation of independent processes by the well-known bakers transformation. Every ergodic, positive-entropy automorphism is measurably isomorphic to some gbt (again generalizing the classical result about Bernoulli shifts), and we show that a large class of gbts satisfying certain continuity restrictions are actually measurably isomorphic to Bernoulli shifts.

Mixing rates and limit theorems for random intermittent maps

We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps

ON SHOCK WAVE SOLUTIONS FOR DISCRETE VELOCITY MODELS OF THE BOLTZMANN EQUATION

T_\alpha

Ulam's Method for Lasota--Yorke Maps with Holes

using the full parameter range

Maximum Entropy Estimates for Risk-Neutral Probability Measures with Non-Strictly-Convex Data

0< \alpha < \infty

Duality and the Computation of Approximate Invariant Densities for Nonsingular Transformations

, in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e.\ smallest

Asymptotic behavior of one-dimensional discrete-velocity models in a slab

\alpha

Ergodic Theory, Open Dynamics, and Coherent Structures

) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (Theorem 1.1) establishes sharp estimates on the position of return time intervals for the \emph{quenched} dynamics. The main applications of this estimate are to \textit{limit laws} (in particular, CLT and stable laws, depending on the parameters chosen in the range

Dynamical conditions for convergence of a maximum entropy method for Frobenius-Perron operator equations

0 < \alpha < 1