Related papers: Asymptotic behavior of divergences and Cameron-Mar…

We study topologically invariant means on $L^{\infty}(\mathbb{R})$, the set of all essentially bounded functions on the real line, and prove that invariance with respect to a single convolution operator is sufficient for a mean to be…

We give the first constant-factor approximation for the Directed Latency problem in quasi-polynomial time. Here, the goal is to visit all nodes in an asymmetric metric with a single vehicle starting at a depot $r$ to minimize the average…

We prove a pointwise ergodic theorem for quasi-probability-measure-preserving (quasi-pmp) locally countable measurable graphs, equivalently, Schreier graphs of quasi-pmp actions of countable groups. For ergodic graphs, the theorem gives an…

We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting…

We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle…

We prove the following extension of the Wiener--Wintner Theorem in Ergodic Theor and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows $ (X,\mu , T_t)$ and $ f\in L^p (X,\mu)$, there is a set…

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…

The primary purpose of this paper is to study the Wiener-type regularity criteria for non-linear equations driven by integro-differential operators, whose model is the fractional $p-$Laplace equation. In doing so, with the help of tools…

We prove a representation for the support of McKean Vlasov Equations. To do so, we construct functional quantizations for the law of Brownian motion as a measure over the (non-reflexive) Banach space of H\"older continuous paths. By solving…

We introduce the notion of a stationary random manifold and develop the basic entropy theory for it. Examples include manifolds admitting a compact quotient under isometries and generic leaves of a compact foliation. We prove that the…

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless…

Based on the rigorous path integral formulation of Liouville Conformal Field Theory initiated by David-Kupiainen-Rhodes-Vargas on the Riemann sphere and David-Rhodes-Vargas on the torus of modulus $\tau$, we give the exact asymptotic…

We generalize the Beckner's type Poincar\'e inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\mu\star\nu$, where $\mu$ is the reference Gaussian measure and $\nu$ is a probability…

Let X be a quasiprojective manifold given by the complement of a divisor $\bD$ with normal crossings in a smooth projective manifold $\bX$. Using a natural compactification of $X$ by a manifold with corners $\tX$, we describe the full…

The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to…

In this paper we provide a way of taking $L^p$, $p > \frac{m}{2}$ bounds on a $m-$ dimensional Riemannian metric and transforming that into H\"{o}lder bounds for the corresponding distance function. One can think of this new estimate as a…

We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…

We prove that some symetric semi-riemannian manifolds do not admit a proper domain which is divisible by the action of a discrete group of isometries. In other words, if a closed semi-riemannian manifold is locally isometric to such a…

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very…