Related papers: Non-invertible planar self-affine sets
A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and…
In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations. We describe characteristic sets and compute difference…
We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an…
An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
Note by the author: Section 9.3 is added from the more general unpublished manuscript ``A Perturbation Method Leading to Full-Dimension Ergodic Measures on Integral Self-Affine Sets'', (2021) by I. Kirat. Original abstract: An integral…
We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under…
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…
We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
Although jammed granular systems are athermal, several thermodynamic-like descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-\delta$ dimensions and finite in size in $\delta$ dimensions, is fundamentally different from that of…
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets…
A central question in the field of inhomogeneous attractors has been to relate the dimension of an inhomogeneous attractor to the condensation set and associated homogeneous attractor. This has been achieved only in specific settings, with…
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence…