Related papers: On Measure Invariance for a 2-valued Transformatio…

We construct a Gibbs measure for the nonlinear Schrodinger equation (NLS) on the circle, conditioned on prescribed mass and momentum: d \mu_{a,b} = Z^{-1} 1_{\int_T |u|^2 = a} 1_{i \int_T u \bar{u}_x = b} exp (\pm1/p \int_T |u|^p - 1/2…

This paper defines Lebesgue measure preserving Thompson's monoid, denoted by $\mathbb{G}$, which is modeled on Thompson's group $\mathbb{F}$ except that the elements of $\mathbb{G}$ are non-invertible. Moreover, it is required that the…

Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on…

We formulate a general statement of the problem of defining invariant measures with certain properties and suggest an ergodic method of perturbations for describing such measures.

We characterize the Borel measures $\mu$ on $\mathbb{R}$ for which the associated dyadic Hilbert transform, or its adjoint, is of weak-type $(1,1)$ and/or strong-type $(p,p)$ with respect to $\mu$. Surprisingly, the class of such measures…

We adopt the standard definition of diffeomorphism for Regge gravity in D=2 and give an exact expression of the Liouville action in the discretized case. We also give the exact form of the integration measure for the conformal factor. In…

In a recent paper, 8 semileptonic parameters were defined to specify the most general Lorentz-invariant spin correlation functions for 2-body tau decays. These parameters can be used to search for anomalous longitudinal-versus transverse…

In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calder\'on-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces $(X,…

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization…

We show existence of an infinitesimally invariant measure $m$ for a large class of divergence and non-divergence form elliptic second order partial differential operators with locally Sobolev regular diffusion coefficient and drift of some…

For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$ diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tilde\Lambda)$…

Let $f$ be an holomorphic endomorphism of $\mathbb{P}^k$ and $\mu$ be its measure of maximal entropy. We prove an Almost Sure Invariance Principle for the systems $(\mathbb{P}^k,f,\mu)$. Our class $\cal{U}$ of observables includes the…

We study weighted Helmholtz--Hodge decompositions of drift vector fields associated with second-order diffusion operators on $\mathbb{R}^d$, $d\ge 2$. Given a decomposition of the form \[ \mathbf{G}=A\nabla\Phi+\mathbf{B}, \] we relate the…

Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure $\mu_0$ on self-avoiding loops in ${\mathbb C} \setminus\{0\}$ which surround $0$. Our first major objective is…

A conjecture of Ulam states that the standard probability measure $\pi$ on the Hilbert cube $I^\omega$ is invariant under the induced metric $d_a$ when the sequence $a = \{ a_i \}$ of positive numbers satisfies the condition…

It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz…

One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…

We show the existence of invariant ergodic $\sigma$-additive probability measures with full support on $X$ for a class of linear operators $L: X \to X$, where $L$ is a weighted shift operator and $X$ either is the Banach space…

We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the…