Related papers: Algebraic decay in hierarchical graphs
Operators are induced on fermion and zeon algebras by the action of adjacency matrices and combinatorial Laplacians on the vector spaces spanned by the graph's vertices. Properties of the algebras automatically give information about the…
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…
In this paper, we study the one-level Friedrichs model with using the quantum time super-operator that predicts the excited state decay inside the continuum. Its survival probability in long time limit is an algebraically decreasing…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance \sigma^2. We show that the statistics of the gap d_{k,n}=M_{k,n}…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
The quantum walk differs fundamentally from the classical random walk in a number of ways, including its linear spreading and initial condition dependent asymmetries. Using stationary phase approximations, precise asymptotics have been…
Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…
We investigate the emergence of spanning structures in sparse pseudo-random $k$-uniform hypergraphs, using the following comparatively weak notion of pseudo-randomness. A $k$-uniform hypergraph $H$ on $n$ vertices is called…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…