相关论文: Duality in percolation via outermost boundaries II…

Tile $\mathbb{R}^2$ into disjoint unit squares $\{S_k\}_{k \geq 0}$ with the origin being the centre of $S_0$ and say that $S_i$ and $S_j$ are star adjacent if they share a corner and plus adjacent if they share an edge. Every square is…

Tile \(\mathbb{R}^2\) into disjoint unit squares \(\{S_k\}_{k \geq 0}\) with the origin being the centre of \(S_0\) and say that \(S_i\) and \(S_j\) are star adjacent if they share a corner and plus adjacent if they share an edge. Every…

Tile (\mathbb{R}^2\) into disjoint unit squares (\{S_k\}_{k \geq 0}\) with the origin being the centre of \(S_0\) and say that (S_i\) and (S_j\) are star adjacent if they share a corner and plus adjacent if they share an edge. Every square…

Tile \(\mathbb{R}^2\) into disjoint unit squares \(\{S_k\}_{k \geq 0}\) with the origin being the centre of \(S_0\) and say that \(S_i\) and \(S_j\) are star-adjacent if they share a corner and plus-adjacent if they share an edge. Every…

In this paper we consider a connected planar graph $G$ and impose conditions that results in $G$ having a percolation lattice-like cellular structure. Assigning each cell of $G$ to be either occupied or vacant, we describe the outermost…

In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary…

In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the series, we present duality theorems for combinations of stars…

We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A…

We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…

We give a generalization of the duality of a zero-dimensional complete intersection to the case of one-dimensional almost complete intersections, which results in a {\em Gorenstein module} $M=I/J$. In the real case the resulting pairing has…

The concept of star-duality is described for self-similar cut-and-project tilings in arbitrary dimensions. This generalises Thurston's concept of a Galois-dual tiling. The dual tilings of the Penrose tilings as well as the Ammann-Beenker…

We report some novel properties of a square lattice filled with white sites, randomly occupied by black sites (with probability $p$). We consider connections up to second nearest neighbours, according to the following rule. Edge-sharing…

In this paper we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times with scaling exponent 3/2, and we…

We identify a class of point-particle models that exhibit a target-space duality. This duality arises from a construction based on supersymmetric quantum mechanics with a non-vanishing central charge. Motivated by analogies to string…

Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation…

We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…

In oscillating stars, mixed modes have p-mode character in the envelope and g-mode character in the core. They are observed in subgiants and red giants, in which the large density gradient outside the core effectively divides the star into…

We divide the circular boundary of a hyperbolic lattice into four equal intervals, and study the probability of a percolation crossing between an opposite pair, as a function of the bond occupation probability p. We consider the {7,3}…

The travel times of light signals between two antipodal points on the surface of a compact star are calculated for two different trajectories: a straight line that passes through the center of the star and a semi-circular trajectory that…