Related papers: Intermittency generated by attracting and weakly r…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…
Transitions from reversible to irreversible or fluctuating states above a critical density and shear amplitude have been extensively studied in non-thermal cyclically sheared suspensions and amorphous solids. Here, we propose that the same…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
On the basis of a lattice gas model and the convolution formula with cell construction scheme, we demonstrate that intermittency in the rapidity-space with respect to the scaled moments comes from a phase transition between ordered phase…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
In the present paper, we introduce a new kind of $p$-adic measures for $q+1$-state Potts model, called {\it $p$-adic quasi Gibbs measure}. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…
In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated…
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…
For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the main properties of strong chain recurrent sets. We then…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacement (FRI). For the high intensity regime, we show the existence of a critical fiber length, and give the exact asymptotic of it as…
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…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…