Related Experiment Video
Updated: May 6, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Asymptotic behaviour of random walks with correlated temporal structure
Marcin Magdziarz1, Władysław Szczotka, Piotr Zebrowski
1Hugo Steinhaus Center , Institute of Mathematics and Computer Science, Wrocław University of Technology , Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland.
Abstract:
We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions. We derive the corresponding diffusion limit and prove its subdiffusive character. Analysing the set of corresponding coupled Langevin equations, we verify the speed of relaxation, Einstein relations, equilibrium distributions, ageing and ergodicity breaking.
Related Concept Videos
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Random Error
Correlation
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Stability of structures
Central Limit Theorem
The sample size, n, that...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

