相关论文: Proximality of multidimensional $\mathscr{B}$-free…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
We present two constructions of projective systems of measures associated to discretizations of free scalar Euclidean quantum fields. The first one is obtained using only purely combinatorial data and applies to free massless scalar fields…
We prove some new statements on the distribution of $\mathcal{B}$-free numbers in short intervals. In particular, we show an asymptotic result for the variance of the number of $\mathcal{B}$-free integers in random short intervals which…
BMS symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in General Relativity, BMS symmetries have also been…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
Recently, the topics of many-body localization (MBL) and one-dimensional strongly interacting few-body systems have received a lot of interest. These two topics have been largely developed separately. However, the generality of the latter…
We discuss the onset of many body localisation in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups depending whether spatial disorder is…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
The class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is…
We prove that the Lipschitz-free space over a countable compact metric space is isometric to a dual space and has the metric approximation property.
Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which…
We establish the most general form of the discrete elasticity of a 2D triangular lattice embedded in three dimensions, taking into account up to next-nearest neighbour interactions. Besides crystalline system, this is relevant to biological…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Many-body localization (MBL) features are studied here for a large spin chain model with long range interactions. The model corresponds to cold atoms placed inside a cavity and driven by an external laser field with long range interactions…
We consider five-dimensional domain-wall solutions which arise from a sphere reduction in M-theory or string theory and have the higher-dimensional interpretation as the near-horizon region of p-branes in constant, background B fields. We…
The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…