Related papers: Entropy Theory for Random Walks on Lie Groups
We study the local entropy production rate and the local entropy flow in active systems composed of non-interacting run-and-tumble particles in a thermal bath. After providing generic time-dependend expressions, we focus on the stationary…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
We investigate the R\'enyi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the R\'enyi entropy, for Poisson-Bernoulli variables. As…
We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G \wr S_n for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P. Thouvenot about completely positive…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
Let $G$ be a countable group and $\mu$ a probability measure on $G$. We build a new framework to compute asymptotic quantities associated with the $\mu$-random walk on $G$, using methods from harmonic analysis on groups and Banach space…
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…
We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
Human communication is commonly represented as a temporal social network, and evaluated in terms of its uniqueness. We propose a set of new entropy-based measures for human communication dynamics represented within the temporal social…
In this work, we apply information theory inspired methods to quantify changes in daily activity patterns. We use in-home movement monitoring data and show how they can help indicate the occurrence of healthcare-related events. Three…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…
We study the independence density for finite families of finite tuples of sets for continuous actions of discrete groups on compact metrizable spaces. We use it to show that actions with positive naive entropy are Li-Yorke chaotic and…
In the study of aperiodic order via dynamical methods, topological entropy is an important concept. In this paper, parts of the theory, like Bowen's formula for fibre wise entropy or the independence of the definition from the choice of a…