Related papers: Fixed-boundary octagonal random tilings: a combina…
Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
In this paper we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot's embedding for growing…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
This paper is based on the study of random lozenge tilings of non-convex polygonal regions with interacting non-convexities (cuts) and the corresponding asymptotic kernel as in [3] and [4] (discrete tacnode kernel). Here this kernel is used…
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…