Related papers: Universal Attractors of Reversible Aggregate-Reorg…
Using dynamic renormalization group we study the transport in driven diffusive systems in the presence of quenched random drift velocity with long-range correlations along the transport direction. In dimensions $d\mathopen< 4$ we find fixed…
We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties,…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…
We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
Breakdown of time-reversal symmetry is a defining property of non-equilibrium systems, such as active matter, which is composed of units that consume energy. We employ a formalism that allows us to derive a class of identities associated…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
Foundational work on the Lottery Ticket Hypothesis has suggested an exciting corollary: winning tickets found in the context of one task can be transferred to similar tasks, possibly even across different architectures. This has generated…
We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one dimensional ring, where the walkers hop to their nearest neighbor with a bias $\epsilon$. For…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…
The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of…
Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design…
We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
We present some exact results on the behavior of Branching and Annihilating Random Walks, both in the Directed Percolation and Parity Conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the…