Related papers: Self-avoiding walks and the Fisher transformation

We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…

Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…

We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the return time to cylinders is given by a step function. We…

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is…

A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using…

Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…

A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or gets extinct. The outcome naturally depends on the…

We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain…

Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be…

We study terminally attached self-avoiding walks and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide strong numerical evidence supporting a scaling relation between self-avoiding walks,…

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…

We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x…

The quadratic embedding constant (QEC) of a finite, simple, connected graph originated from the classical work of Schoenberg [Ann. of Math., 1935] and [Trans. Amer. Math. Soc., 1938] on Euclidean distance geometry. In this article, we study…

In this study, considering the Fisher information metric (Fisher metric) given by a specific form, which is the form of weights in statistical physics, we rewrite the Einstein-Hilbert (EH) action. Then, determining the transformation rules…

This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…

We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of…