相关论文: Asymptotic geometry of discrete interlaced pattern…
We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based…
We analyse the local geometric structure of self-similar sets with open set condition through the study of the properties of a distinguished family of spherical neighbourhoods, the typical balls. We quantify the complexity of the local…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
This study is about the properties of the sets of objects associated in a structure resulting from multiple-processes involving chance as are materials whose texture is unordered and random. Being a paper scientist the author refers to the…
Let $P$ be the Gelfand--Tsetlin polytope defined by the skew shape $\lambda/\mu$ and weight $w$. In the case corresponding to a standard Young tableau, we completely characterize for which shapes $\lambda/\mu$ the polytope $P$ is integral.…
Given finite configurations $P_1, \dots, P_n \subset \mathbb{R}^d$, let us denote by $\mathbf{m}_{\mathbb{R}^d}(P_1, \dots, P_n)$ the maximum density a set $A \subseteq \mathbb{R}^d$ can have without containing congruent copies of any…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary…
We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics include, in particular, a multi-layer extension of TASEP and…
Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field,…
A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental…
In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision…
We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and allied systems. We show that this distribution is governed by a…
Natural materials often feature a combination of soft and stiff phases, arranged to achieve excellent mechanical properties, such as high strength and toughness. Many natural materials have even independently evolved to have similar…
The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
Light scattering by dust particles is often modeled assuming the dust is spherical for numerical simplicity and speed. However, real dust particles have highly irregular morphologies that significantly affect their scattering properties. We…
Needles at different orientations are placed in an i.i.d. manner at points of a Poisson point process on $\mathbb R^2$ of density $\lambda$. Needles at the same direction have the same length, while needles at different directions maybe of…
We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing…
We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect…