Related papers: Delocalization-localization dynamical phase transi…
We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a…
Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this…
We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase…
Dynamic graph representation learning plays a crucial role in understanding evolving behaviors. However, existing methods often struggle with flexibility, adaptability, and the preservation of temporal and structural dynamics. To address…
In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states…
We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…
The possibility of having a delocalization transition in the 1D de Moura-Lyra class of models (having a power-spectrum $\propto q^{-\alpha})$ has been the object of a long standing discussion in the literature, filled with ambiguities. In…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems which fail to achieve thermal equilibrium. From a quantum information perspective, the fingerprint of this…
Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal…