相关论文: Random "dyadic" lattice in geometrically doubling …

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…

The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed…

For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and…

We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces…

Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…

We review and possibly add some new variant to the existing derivations of the formula for the area of Jordan lattice polygons drawn on two-dimensional lattices. The formula is known as Pick's theorem and is related to the number theory…

We solve several open problems concerning integer points of polytopes arising in symplectic and algebraic geometry. In this direction we give the first proof of a broad case of Ewald's Conjecture (1988) concerning symmetric integral points…

In some recent papers the classical `splitting necklace theorem' is linked in an interesting way with a geometric `pattern avoidance problem'. We explore the topological constraints on the existence of a (relaxed) measurable coloring of R^d…

Two-dimensional lattices provide the arena for many physics problems of essential importance, a non-trivial symmetry in such lattices will help to reveal the underlying physics. Whether there is a directional scaling for the 2D lattices is…

This paper develops geographic-style maps containing 2D lattices in all known crystals parameterised by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The…

Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a…

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the…

We present a simple lattice formulation of two-dimensional $\mathcal{N}=(2,2)$ $U(k)$ supersymmetric QCD (SQCD) with $N$ matter multiplets in the fundamental representation. The construction uses compact gauge link variables and exactly…

A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes,…

We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable…

In the large-$N$ and strong-coupling limit, maximally supersymmetric SU($N$) Yang--Mills theory in $(2 + 1)$ dimensions is conjectured to be dual to the decoupling limit of a stack of $N$ D$2$-branes, which may be described by IIA…

We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze…

Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…

We study the typical behavior of the size of the ratio set $A/A$ for a random subset $A\subset \{1,\dots , n\}$. For example, we prove that $|A/A|\sim \frac{2\text{Li}_2(3/4)}{\pi^2}n^2 $ for almost all subsets $A \subset\{1,\dots ,n\}$. We…