Related papers: Generating Functions of Random Walks on Graphs
We address the enumeration of walks with small steps confined to a two-dimensional cone, for example the quarter plane, three-quarter plane or the slit plane. In the quarter plane case, the solutions for unweighted step-sets are already…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of sets of steps from a predefined set such that all possible…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. At each step, a nondeterministic walk draws a random set of steps from a predefined set of sets and explores all possible extensions in parallel.…
We have found an analytic expression for the multivariate generating function governing all n-point statistics of random multiplicative cascade processes. The variable appropriate for this generating function is the logarithm of the energy…
We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given…
We analyze a random walk strategy on undirected regular networks involving power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a `simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks' with…
Random transvections generate a walk on the space of symplectic forms on $\mathbf{F}_q^{2n}$. The main result is establishing cutoff for this Markov chain. After $n+c$ steps, the walk is close to uniform while before $n-c$, it is far from…
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
A table of sums useful for generating function applications (discrete Laplace transforms or z-transforms). Related definitions and formulas (including Lagrange's expansion), and reference to formulas in Abramowitz and Stegun, Handbook of…
It is shown that the generating function for tree graphs in the "in-in" formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of…
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
We develop entropy and variance results for the product of independent identically distributed random variables on Lie groups. Our results apply to the study of stationary measures in various contexts.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
The paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on $\mathbb{Z}$. This result appears as an extension of the invariance principal theorem for classical random walks on $\mathbb{Z}$ or…
Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Motivated by the harmonic analysis of self-affine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information…