We classify the possible closures of leaves isoperiodic foliation defined on Hodge bundle over moduli space genus $$g\ge 2$$ curves and prove that is ergodic those sets. The results derive from connectedness properties fibers period map Torelli cover space. Some consequences topology Hurwitz spaces primitive branched coverings elliptic are also obtained. To we develop theory augmented space, De...

This paper is concerned with the parameter estimation problem for a class of diffusion process from discrete observations. The approximate likelihood function given by using Riemann sum and an Itˆo to integrals in continuous-time function. consistency maximum estimator asymptotic normality error are proved applying martingale moment inequality, Holder’s Chebyshev B-D-G inequality uniform ergodi...

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...

Let T be a measure-preserving and mixing action of a countable abelian group G on a probability space (X, S, μ) and A a locally compact second countable abelian group. A cocycle c : G × X 7−→ A for T disperses if limg→∞ c(g, ·) − α(g) = ∞ in measure for every map α : G −→ A. We prove that such a cocycle c does not disperse if and only if there exists a compact subgroup A0 ⊂ A such that the comp...

We show that any locally compact group G with polynomial growth is weakly commensurable to some simply connected solvable Lie group S, the Lie shadow of G. We then study the shape of large balls and show, generalizing work of P. Pansu, that after a suitable renormalization, they converge to a limiting compact set which can be interpreted geometrically. As a consequence, we get the volume asympt...

Given an ergodic finite-state Markov chain, let Miw denote the mean time from i to equilibrium, meaning the expected time, starting from i, to arrive at a state selected randomly according to the equilibrium measure w of the chain. John Kemeny observed that Miw does not depend on starting the point i. The common value K = Miw is the Kemeny constant or seek time of the chain. K is a spectral inv...