Related papers: A unified approach to mass transference principle …

We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is the establishment of the propagation of…

We establish a general transference principle for the irrationality measure of points with $\mathbb{Q}$-linearly independent coordinates in $\mathbb{R}^{n+1}$, for any given integer $n\geq 1$. On this basis, we recover an important…

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…

We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a…

We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof…

The recent breakthrough of Guth, Iosevich, Ou, and Wang (2019) on the Falconer distance problem states that for a compact set $A\subset \mathbb{R}^2$, if the Hausdorff dimension of $A$ is greater than $\frac{5}{4}$, then the distance set…

Let $\cS_n(\psi_1,...,\psi_n)$ denote the set of simultaneously $(\psi_1,...,\psi_n)$--approximable points in $\R^n$ and $\cSM_n(\psi)$ denote the set of multiplicatively $\psi$--approximable points in $\R^n$. Let $\cM$ be a manifold in…

Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this…

In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to…

The Isometry Theorem of Chazal et al. and Lesnick is a fundamental result in persistence theory, which states that the interleaving distance between two one-parameter persistence modules is equal to the bottleneck distance between their…

We show that limsup sets generated by a sequence of open sets in compact Ahlfors $s$-regular space $(X,\mathscr{B},\mu,\rho)$ belong to the classes of sets with large intersections with index $\lambda$, denoted by…

Dobi\'nski set $\mathcal{D}$ is an exceptional set for a certain infinite product identity, whose points are characterized as having exceedingly good approximations by dyadic rationals. We study the Hausdorff dimension and logarithmic…

Dempster-Shafer evidence theory is a powerful tool in information fusion. When the evidence are highly conflicting, the counter-intuitive results will be presented. To adress this open issue, a new method based on evidence distance of…

We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…

In 1998, Kleinbock & Margulis established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous…

The Jarn\'ik-Besicovitch theorem is a fundamental result in metric number theory which gives the Hausdorff dimension for limsup sets. We investigate a related problem of estimating the Hausdorff dimension of a liminf set. Let $h>0, \tau\geq…

This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…

We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…

We develop a constant-tracking likelihood theory for two nonregular models: the folded normal and finite Gaussian mixtures. For the folded normal, we prove boundary coercivity for the profiled likelihood, show that the profile path of the…

Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…