Related papers: Automatic continuity of transversal distributions

We show that every homomorphism from the infinite-dimensional unitary or orthogonal group to a separable group is continuous.

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.

In this paper we classify all topological vector spaces with linear topology with the property that all algebraic automorphisms are continuous. Moreover, we prove some properties of these spaces.

In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when it is not true.

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a…

Answering the question of V.I. Oseledets, we present a random variable $\xi$ such that the sum $\xi(x)+a\xi(y)$ has a singular distribution for a set of parameters $a$ dense in $(1, +\infty)$, but for another dense set of parameters, this…

Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property: any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a…

We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous…

We will consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random…

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

We prove that the limit profile of a sequence of reversible Markov chains exhibiting total variation cutoff is a continuous function, under a computable condition involving the spectrum of the transition matrix and the cutoff window.

We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

A tree-strip of finite cone type is the product of a tree of finite cone type with a finite set. We consider random Schr\"odinger operators on these tree strips, similar to the Anderson model. We prove that for small disorder the spectrum…