Intermittency and the central limit theorem

Central limit theorem estimates of anomalous fractal dimensions of self-similar random cascades are studied. It is found that, in general, the normal approximation fails badly. A systematic series of approximations which converges to the exact result (both for the fractal dimensions and for the distribution itself) is derived for the -model. Consequences for the empty bin effect are indicated.Supported by the World Laboratory/HED and the CERN/LAA Projects     

A limit theorem for stochastic acceleration

We consider the motion of a particle in a weak mean zero random force fieldF, which depends on the position,x(t), and the velocity,v(t)= (t). The equation of motion is (t)=F(x(t),v(t), ), wherex(·) andv(·) take values in ^d ,d3, and ranges over some probability space. We show, under suitable mixing and moment conditions onF, that as 0,v (t)v(t/²) converges weakly to a diffusion Markov processv(t), and ² x (t) converges weakly to , wherex=lim ² x (0).     

A limit theorem for turbulent diffusion

We show under some specific conditions that the formal diffusion approximation for the motion of a particle in a random velocity field is valid.     

Coherent state path integral methods and central limit theorem

We consider a coherent state path integral expression originating for example after path integration over a second interacting system and by using a method based on the use of the central limit theorem on the phase of the path integral representation, we extract under certain conditions a closed form for the propagator.     

Modulation bandwidth and noise limit of photoconductive gates

The modulation bandwidth and noise limit of a photoconductive sampling gate are studied by reducing the parasitic capacitance and leakage current of the sampling circuit using an integrated junction field-effect transistor (JFET) source follower. The modulation bandwidth of the photoconductive sampling gate is limited by the external parasitic capacitance, and its efficiency is found to saturate at a laser gating power of about 1 mW. It is determined that the noise of the photoconductive sampling gate is dominated by the photovoltaic current due to the gating laser amplitude fluctuation. A minimum noise level of 4 nV Hz^–1/2 has been measured, and an enhancement in signal-to-noise ratio by a factor of >45 has been achieved after the integration of the source follower with the photoconductive sampling gate. The JFET source follower serves to increase the modulation bandwidth of the photoconductive sampling gate by about 15 times and buffer the charge of the measured signal using its extremely high gate input impedance. The performance of the photoconductive sampling gate in regard to invasiveness and gating efficiency has been optimized, while a picosecond temporal resolution has been maintained and the signal-to-noise performance has been enhanced using a gating laser power as low as 10 W.     

A general central limit theorem for FKG systems

A central limit theorem is given which is applicable to (not necessarily monotonic) functions of random variables satisfying the FKG inequalities. One consequence is convergence of the block spin scaling limit for the magnetization and energy densities (jointly) to the infinite temperature fixed point of independent Gaussian blocks for a large class of Ising ferromagnets whenever the susceptibility is finite. Another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models.     

Quantum noise — A limit in photodetection

This paper attempts to outline the fundamental limits of the photoelectric measurement process, to give a simple picture of how their consequences can be estimated and to describe recent ideas and experimental work on how to use the current understanding of photodetection to make measurements previously thought to be beyond the quantum limit.     

Quantum tunneling and zero-point motion limit of noise fluctuations

It is shown that interpreting the zero-point noise of a resistor as dynamical noise capable of driving a Josephson phase across a potential barrier delivers qualitatively identical results with quantum mechanical tunneling calculation in the overdamped limit.     

Effect of noise and perturbations on limit cycle systems

This paper demonstrates that the influence of noise and of external perturbations on a nonlinear oscillator can vary strongly along the limit cycle and upon transition from limit cycle to stationary point behaviour. For this purpose we consider the role of noise on the Bonhoeffer-van der Pol model in a range of control parameters where the model exhibits a limit cycle, but the parameters are close to values corresponding to a stable stationary point. Our analysis is based on the van Kampen approximation for solutions of the Fokker-Planck equation in the limit of weak noise. We investigate first separately the effect of noise on motion tangential and normal to the limit cycle. The key result is that noise induces diffusion-like spread along the limit cycle, but quasistationary behaviour normal to the limit cycle. We then describe the coupled motion and show that noise acting in the normal direction can strongly enhance diffusion along the limit cycle. We finally argue that the variability of the system's response to noise can be exploited in populations of nonlinear oscillators in that weak coupling can induce synchronization as long as the single oscillators operate in a regime close to the transition between oscillatory and excitatory modes.     

On the local central limit theorem for Gibbs processes

We derive a sufficient condition for the validity of the local central limit theorem for Gibbs processes and their isomorphism with a Bernoulli shift.     

A central limit theorem for the disordered harmonic chain

Using methods introduced by Furstenberg and Tutubalin we prove a central limit theorem for the amplitudes of plane waves travelling in a semi-infinite isotopically disordered harmonic chain. This theorem is applied to the problem of heat conduction in disordered harmonic chains.     

The central limit theorem and the problem of equivalence of ensembles

In this paper we show that the local limit theorem is a consequence of the integral central limit theorem in the case of a Gibbs random field _t ,tZ corresponding to a finite range potential.We apply this theorem to show that the equivalence between Gibbs and canonical ensemble is a consequence of the integral central limit theorem and of very weak conditions on decrease of correlations.Research supported by a C.N.R.-Ak. Nauk. U.R.S.S. fellowship     

The local central limit theorem for a Gibbs random field

We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential.     

Work fluctuation theorem for coloured noise driven open systems

We have studied work fluctuation behaviour in the presence of internal thermal noise as well as external coloured noise. The external coloured noise may have both Gaussian or non-Gaussian characteristics. We have investigated the dependence of position and work fluctuations on the properties of both the environments. For thermal noise driven systems, there is a maximum in the variation of mean square fluctuation of work (MSFW) as a function of damping strength at intermediate times, while at asymptotic long times MSFW monotonically increases in the same damping regime. But for external noise, MSFW monotonically decreases as a function of damping strength at intermediate times, whereas at long times it becomes almost independent of damping strength.Another interesting observation is that for the external noise driven systems, noise correlation time and damping strength have similar roles in the dynamics.     

Geometry of the central limit theorem in the nonextensive case

We uncover geometric aspects that underlie the sum of two independent stochastic variables when both are governed by q-Gaussian probability distributions. The pertinent discussion is given in terms of random vectors uniformly distributed on a p-sphere.