Related papers: Haruspicy 3: The directed bond-animal generating f…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations […
Two one-dimensional Luttinger liquid systems coupled by Hund's coupling are studied by the renormalization group and the non-abelian bosonization methods. It is found that the Hund's coupling is always relevant irrespective of the repulsive…
Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally…
We report on the status of the conjecture of Bousquet-M\'elou and Mishna that the univariate counting generating function of a small-step quarter-plane lattice model is D-finite if and only if the group of the walk is finite. While the…
More than 15 years ago Guttmann and V\"oge [J. Statist. Plann. Inference, {\bf 101}, 107 (2002)], introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied…
We consider the nonabelian sandpile model defined on directed trees by Ayyer, Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to the special case of a one-dimensional lattice of $n$ sites which has open…
We examine the question of which finitely generated groups act properly on a finite product of simplicial trees, considering both arbitrary trees and where all trees are locally finite. In the second case we present evidence in favour of…
We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice $\Lambda \subseteq \mathbb{R}^d$ inside the $d$-sphere of radius $R$. In contrast to…
We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2…
We study homoclinic snaking of one-dimensional, localised states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned…
This paper studies residual finiteness of lattices in the universal cover of $\mathrm{PU}(2,1)$ and applications to the existence of smooth projective varieties with fundamental group a cocompact lattice in $\mathrm{PU}(2,1)$ or a finite…
To analyse how diffusion models learn correlations beyond Gaussian ones, we study the behaviour of higher-order cumulants, or connected n-point functions, under both the forward and backward process. We derive explicit expressions for the…
We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
Most legged robots are built with leg structures from serially mounted links and actuators and are controlled through complex controllers and sensor feedback. In comparison, animals developed multi-segment legs, mechanical coupling between…
We investigate the static and dynamical behavior of 1D interacting fermions in disordered Hubbard chains, contacted to semi-infinite leads. The chains are described via the repulsive Anderson-Hubbard Hamiltonian, using static and…
We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…
In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular,…
We consider the Directed Spanning Forest (DSF) constructed as follows: given a Poisson point process N on the plane, the ancestor of each point is the nearest vertex of N having a strictly larger abscissa. We prove that the DSF is actually…