Related papers: Large deviations in models of growing clusters wit…
We describe the cluster of large deviations events that arise when one such large deviations event occurs. We work in the framework of an infinite moving average process with a noise that has finite exponential moments.
Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the…
A recent study of nonextensive phase transitions in nuclei and nuclear clusters needs a probability model compatible with the appropriate Hamiltonian. For magnetic molecules a representation of the evolution by a Markov process achieves the…
The probability distribution of the maximum $M_t$ of a single resetting Brownian motion (RBM) of duration $t$ and resetting rate $r$, properly centred and scaled, is known to converge to the standard Gumbel distribution of the classical…
At the critical point, the probability density function of the Ising magnetization is believed to decay like $\exp{(-x^{\delta+1})}$, where $\delta$ is the Ising critical exponent that controls the decay to zero of the magnetization in a…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
We consider the process of reaching the final state in the coevolving voter model. There is a coevolution of state dynamics, where a node can copy a state from a random neighbor with probabilty $1-p$ and link dynamics, where a node can…
The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along…
The large scale gravitational potential distribution and its influence on the large-scale matter clustering is considered on the basis of six simulations. It is found that the mean separation between zero levels of the potential along…
We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction $X+Y \to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent simple…
The classic Vicsek model [Phys.Rev.Lett. {\bf75},1226(1995)] is studied in the regime of very low noise intensities, which is shown to be characterized by a cluster (MC) that contains a macroscopic fraction of the system particles. It is…
We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature…
The Poisson--Dirichlet distribution arises in many different areas. The parameter $\theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $\theta$ approaching…
A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
We explore the decay of turbulence and magnetic fields generated by fluctuation dynamo action in the context of galaxy clusters where such a decaying phase can occur in the aftermath of a major merger event. Using idealized numerical…
We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this…
We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down…
Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…