Research
Research
Research
Research
180+ open-access research outputs.
We study the almost surely finite random variable $S$ defined by the distributional fixed-point equation \[ S \stackrel{d}{=} 1 + \max\{US', (1-U)S''\}, \qquad U \sim \mathrm{Unif}(0,1), \] where $S'$…
This paper extends the study of fringe trees in random plane trees with a given degree statistic. While previous work established the asymptotic normality of the count of fringe trees isomorphic to a …
Let $\g$ be a simple complex Lie algebra of type $G_2$, $F_4$, or $E_8$, and let $G$ be the unique connected simply connected Lie group with $\mathrm{Lie}(G)=\g$ with compact real form $K$. We prove a…
The Power-Relaxed Greedy Algorithm (PRGA) was introduced as a generalization of the so called Relaxed Greedy Algorithm, introduced by DeVore and Temlyakov, by replacing the relaxation parameter $1/m$ …
The seminal work of Daubechies, DeVore, Foucart, Hanin, and Petrova introduced in 2022 a sequence of univariate piece-wise linear functions, which resemble the classical Fourier basis and which, at th…
In this note, we study a quantitative extension of the John-Nirenberg inequality for the Hardy-Littlewood maximal function of a $\operatorname{BMO}$ function. More precisely, for every nonconstant loc…
This paper analyzes a class of recursive distributional equations (RDE's) proposed by Gurel-Gurevich [17] and involving a bias parameter $p$, which includes the logarithm of the resistance of the seri…
Motivated by questions in social networks, distributed computing and probabilistic combinatorics, the last few years have seen increasing interest in network evolution models where new vertices enteri…
This article offers a motivating travel guide towards the Jordan normal form, one of the highlights in courses on linear algebra or advanced mathematics. Its itinerary is characterized by a focus on c…
We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies. On the one hand, when the prey is uniformly distributed, the best possible strategy for th…
We prove a triangular decomposition theorem for the lower crystal lattice $\mathcal{O}_{t}^{A_{0}}(G)$ of the quantized function algebra $\mathcal{O}_{t}(G)$, where $G$ is a connected simply connected…
Binary search trees (BSTs) are fundamental data structures whose performance is largely governed by tree height. We introduce a block model for constructing BSTs by embedding internal BSTs into the no…
Let $X$ be a ball Banach function space on $\mathbb{R}^n$, $k\in\mathbb{N}$, $h\in\mathbb{R}^n$, and $\Delta^k_h$ denote the $k${\rm th} order difference. In this article, under some mild extra assump…
We study Lam's reduced random walk in a hyperbolic triangle group, which we view as a random walk in the upper half-plane. We prove that this walk converges almost surely to a point on the extended re…
We consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO…
We prove precise conditional estimates for the third moment of the logarithm of the Riemann zeta function, refining what is implied by the Selberg central limit theorem, both for the real and imaginar…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring…
This paper examines the limiting variance of nearest neighbor matching estimators for average treatment effects with a fixed number of matches. We present, for the first time, a closed-form expression…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flo…
The initial part of this paper is devoted to the notion of pseudo-seminorm on a vector space $E$. We prove that the topology of every topological vector space is defined by a family of pseudo-seminorm…
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