Related papers: Recent progress on the Random Conductance Model

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…

Robust open-loop steering of a finite-dimensional quantum system is a central problem in a growing number of applications of information engineering. In the present paper, we reformulate the problem in the classical control-theoretic…

We extend existing connections between random walks, branching processes, and spatial branching processes, and their respective scaling limits, to include processes in dependent random environments. More specifically, we prove new scaling…

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

In this paper we consider random walks on Galton-Watson trees with random conductances. On these trees, the distance of the walker to the root satisfies a law of large numbers with limit the effective velocity, or speed of the walk. We…

We consider a weighted random walk on the backbone of an oriented percolation cluster. We determine necessary conditions on the weights for Brownian scaling limits under the annealed and the quenched law. This model is a random walk in…

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of Large Numbers for the position of the walker, properly…

The quantitative measurement of how and when we experience surprise has mostly remained limited to laboratory studies, and its extension to naturalistic settings has been challenging. Here we demonstrate, for the first time, how…

The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…

This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…

This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…

Novelty attracts attention like popularity. Hence predicting novelty is as important as popularity. Novelty is the side effect of competition and aging in evolving systems. Recent behavior or recent link gain in networks plays an important…

A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…

We review recent works where we have shown that disorder relevance is closely related to the existence of non-trivial, random continuum limits

The conductance through a finite quantum dot network is studied as a function of inter-dot coupling. As the coupling is reduced, the system undergoes a transition from the antidot regime to the tight binding limit, where Coulomb resonances…

We present a planning and control framework for physics-based manipulation under uncertainty. The key idea is to interleave robust open-loop execution with closed-loop control. We derive robustness metrics through contraction theory. We use…

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient…

This paper explores the properties of adaptive systems with closed-loop reference models. Using additional design freedom available in closed-loop reference models, we design new adaptive controllers that are (a) stable, and (b) have…