Related papers: A general principle for Hausdorff measure
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
The main goal of this work is to give new and precise generalizations to various classes of plurisubharmonic functions of the classical minimum modulus principle for holomorphic functions of one complex variable, in the spirit of the famous…
The concept of uniform tangent sets was introduced and discussed in [3 - Krastanov, Ribarska, SIAM J. Control Optim., 55(3), 2017]. This study is devoted to their further investigation and to generalization of the abstract Lagrange…
In this paper, we first provide a criterion on uniform large deviation principles (ULDP) of stochastic differential equations under Lyapunov conditions on the coefficients, which can be applied to stochastic systems with coefficients of…
We generalize Petridis's new proof of Pl\"unnecke's graph inequality to graphs whose vertex set is a measure space. Consequently, this gives new Pl\"unnecke inequalities for measure preserving actions which enable us to deduce, via a…
We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set…
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…
We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image…
We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…
In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The…
We associate to a test configuration of an ample line bundle a filtration of the section ring of the line bundle. Using the recent work of Boucksom-Chen we get a concave function on the Okounkov body whose law with respect to Lebesgue…
We establish a multidimensional fractal transference principle for digit-restricted sets associated with subsets of $\mathbb{N}^d$, extending the one-dimensional framework of Nakajima--Takahasi, Adv. Math. (2025). We develop general…
In this paper we improve estimates of Jarnik and Apfelbeck for uniform Diophantine exponents of transposed systems of linear forms and generalize to the case of an arbitrary system the estimates of Laurent and Bugeaud for individual…
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent…
A classical theorem of Menshov states that every measurable function can redefined on a set of arbitrarily small Lebesgue measure, so that the resulting function has uniformly convergent Fourier series. We prove that the same is true if we…
We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapunov exponents. Central to the discussion is the…
The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited,…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
A set of chords of a circle of given radius is represented as a metric space w.r.t. a metric introduced by Hausdorf. The form of open and closed balls with respect to this metric is established. We consider a family of Hausdorff outer…
We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish…