相关论文: Generalized approach to the non-backtracking lace …
We examine the percolation model in $\mathbb{Z}^d$ by an approach involving lattice animals, in which their relevant characteristic is surface-area-to-volume ratio. Two critical exponents are introduced. The first is related to the growth…
We present a new proof of $|x|^{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\mathbb{Z}^d$ above the upper critical dimension, based on the lace expansion and assuming appropriate…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
Recently, Holmes and Perkins identified conditions which ensure that for a class of critical lattice models the scaling limit of the range is the range of super-Brownian motion. One of their conditions is an estimate on a spatial moment of…
We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above…
We investigate oriented bond-site percolation on the planar lattice in which entire columns are stretched. Generalising recent results by Hil\'ario et al., we establish non-trivial percolation under a $(1+\varepsilon)$-th moment condition…
We study in detail the postselection problem in a specific model: bosons hopping on a lattice subjected to continuous local measurements of quadrature observables. We solve the model analytically and show that the postselection overhead can…
We expand a discrete--time lattice sine--Gordon equation on multiple lattices and obtain the partial difference equation which governs its far field behaviour. Such reduction allow us to obtain a new completely discrete nonlinear…
We describe a percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Tissues are considered as structures made of regular healthy,…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice…
Expansion Microscopy is a super-resolution technique in which physically enlarging samples in an isotropic manner increases inter-molecular distances such that nano-scale structures can be resolved using light microscopy. This is…
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
This paper proposes a parallel computation strategy and a posterior-based lattice expansion algorithm for efficient lattice rescoring with neural language models (LMs) for automatic speech recognition. First, lattices from first-pass…
The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now…
Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
We conjecture an integrability and linearizability test for dispersive Z^2-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation…
We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly…
We analyze the motion of a single hole on a N\'eel background, neglecting spin fluctuations. Brinkman and Rice studied this problem on a cubic lattice, introducing the retraceable-path approximation for the hole Green's function, exact in a…