Related papers: Symmetric random walks on certain amalgamated free…
We have developed an approach to calculate the single-particle Green function of a one-dimensional many-body system in the strongly localized limit at zero temperature. Our approach, based on the locator expansion, sums the contributions of…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Given a random walk $(S_n)$ with typical step distributed according to some fixed law and a fixed parameter $p \in (0,1)$, the associated positively step-reinforced random walk is a discrete-time process which performs at each step, with…
We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants…
We construct random Morse functions on surfaces by random walk and compute related distributions. We study the space of Morse functions through these random variables. We consider subspaces characterized by the surfaces with boundary…
Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…
We revisit a family of integrals that delude intuition, and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals…
We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…
We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
Cubical complexes are metric spaces constructed by gluing together unit cubes in an analogous way to the construction of simplicial complexes. We construct Brownian motion on such spaces, define random walks, and prove that the transition…
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs we derive a new variational formula…
Inspired by constructions of Kova\v{c}evi\'{c}, we introduce the amalgamated free product of circle actions, obtained by blowing up two actions along prescribed orbits and rearranging the inserted intervals. Under natural orbit and index…
A Random walk labeling of a graph $G$ is any labeling of $G$ that could have been obtained by performing a random walk on $G$. Continuing two recent works, we calculate the number of random walk labelings of perfect trees, combs, and double…
Let $\Gamma$ be a non-elementary relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure $\mu$ on $\Gamma$ and a probability measure $\nu$ on $\mathbb{N}$ with…
We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the Diestel-Leader graph $DL(q,r)$, where $q,r \ge 2$. The latter is the horocyclic product of two homogeneous trees with…
We define two actions of the infinite symmetric group on the set of words on positive integers, called the free and parking quasi-symmetrizing actions, whose invariants are respectively the elements of the Hopf algebras $\textbf{FQSym}^*$…
We consider random non-hermitean matrices in the large $N$ limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this…
We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.