Related papers: Strange Random Topology of the Circle
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of…
The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of…
We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least…
Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral…
The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. We study the higher-order connectivity of such a network by investigating the topological…
We investigate a random normal matrix model with eigenvalues forced to be in the droplet, the support of the equilibrium measure associated with an external field. For radially symmetric external fields, we show that the fluctuations of the…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
We present Euler Characteristic Surfaces as a multiscale spatiotemporal topological summary of time series data encapsulating the topology of the system at different time instants and length scales. Euler Characteristic Surfaces with an…
The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavy-tailed degree distribution, has a (low) diameter that effectively remains…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
We define a category of filtered topological spaces and explore some of its homotopy theoretic properties, including a filtered analogue of CW approximation. With this, we define and study a filtered (weighted) variant of the Euler…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
We consider the multiparameter random simplicial complex on a vertex set $\{ 1,\dots,n \}$, which is parameterized by multiple connectivity probabilities. Our key results concern the topology of this complex of dimensions higher than the…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…