Related papers: Spanning forests on the Sierpinski gasket

We prove that the uniform spanning forests of $\mathbb{Z}^d$ and $\mathbb{Z}^{\ell}$ have qualitatively different connectivity properties whenever $\ell >d \geq 4$. In particular, we consider the graph formed by contracting each tree of the…

We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…

For a harmonic function on a tree with random walk whose transition probabilities are bounded between two constants in (0,1/2), it is known that the radial and stochastic properties of convergence, boundedness and finiteness of energy are…

We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity…

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained…

The arboreal gas is the random (unrooted) spanning forest of a graph in which each forest is sampled with probability proportional to $\beta^{\# \text{edges}}$ for some $\beta\geq 0$, which arises as the $q\to 0$ limit of the…

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…

We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction,…

On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…

We consider query trees of graphs with degree bounded by a constant, $d$. We give simple proofs that the size of a query tree is constant in expectation and $2^{O(d)}\log{n}$ w.h.p.

We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$ decreasing…

We prove the continuity of asymptotic entropy, as a function of the step distribution, among non-degenerate probability measures with finite Shannon entropy on the free solvable group $S_{d,m}$ of rank $d\ge 3$ and derived length $m\ge 2$.

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the $1/k$ grids. The intersection of two cells can be…

Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by…

We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…

We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. By doing so, over the discretizations, we relate the…

We study boundary value problems for harmonic functions on certain domains in the level-$l$ Sierpinski gaskets $\mathcal{SG}_l$($l\geq 2$) whose boundaries are Cantor sets. We give explicit analogues of the Poisson integral formula to…

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD)…

The discrete Chebyshev polynomials $t_n(x,N)$ are orthogonal with respect to a distribution function, which is a step function with jumps one unit at the points $x=0,1,..., N-1$, N being a fixed positive integer. By using a double integral…

We compute the first three terms of the 1/d expansions for the growth constants and one-point functions of nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd, with rigorous error estimates. The proof uses…