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Irene Giardina

Publications and source records attributed to Irene Giardina.

71 records · Page 4Linked to original sources
arXiv2001

Microscopic Models for Long Ranged Volatility Correlations

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy, or a more sophisticated version that includes some price dynamics. We show that real market data can be surprisingly well accounted for by these simple models.

cond-mat.dis-nn↗
arXiv2001

Role of saddles in mean-field dynamics above the glass transition

Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy. Here we further develop this program in the context of a mean-field model, by analytically studying the properties of the closest saddle point to an equilibrium configuration of the system. We prove that when the glass transition is approached the energy of the closest saddle goes to the threshold energy, defined as the energy level below which the degree of instability of the typical stationary points vanishes. Moreover, we show that the distance between a typical equilibrium configuration and the closest saddle is always very small and that, surprisingly, it is almost independent of the temperature.

cond-mat.stat-mech↗
arXiv2001

Energy landscape of a Lennard-Jones liquid: Statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperature Tc.

cond-mat.stat-mech↗
arXiv2000

On a universal mechanism for long ranged volatility correlations

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be surprisingly well accounted for by these simple models.

cond-mat↗
arXiv2000

Saddles on the potential energy landscape of a Lennard-Jones liquid

By means of molecular dynamics simulations, we study the stationary points of the potential energy in a Lennard-Jones liquid, giving a purely geometric characterization of the energy landscape of the system. We find a linear relation between the degree of instability of the stationary points and their potential energy, and we locate the energy where the instability vanishes. This threshold energy marks the border between saddle-dominated and minima-dominated regions of the energy landscape. The temperature where the potential energy of the Stillinger-Weber minima becomes equal to the threshold energy turns out to be very close to the mode-coupling transition temperature.

cond-mat.stat-mech↗
arXiv2000

Population dynamics in a random environment

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory like argument to understand qualitatively this non trivial diffusive behaviour. A one loop RG analysis close to the critical dimension d_c=2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.

cond-mat↗
arXiv2000

Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''

We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper [Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that the effects of the temperature in the Thermal Minority Game ``can be eliminated by time rescaling'' and consequently the behaviour is ``independent of T'' has no general validity.

cond-mat.stat-mech↗
arXiv1999

A new approach for the analytic computation of the Instantaneous Normal Modes spectrum

In the context of the Instantaneous Normal Mode approach, the spectrum of the Hessian of Hamiltonian is a key quantity to describe liquids behaviour. The determination of the spectrum represents a major task for theoretical studies, and has been addressed recently in various works. In this paper a new approach for the analytic computation of the Hessian spectrum is presented. The one dimensional case for a system of particles interacting via a purely repulsive potential at low density is analyzed in details and the spectrum is computed exactly also in the localized sector. Finally, the possible extensions of the method are discussed, together with a comparison with different approaches to the problem.

cond-mat.stat-mech↗
arXiv1999

Index Distribution of Random Matrices with an Application to Disordered Systems

We compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics of disordered systems, where the second derivative of the potential energy (the Hessian) is a random matrix whose negative eigenvalues measure the degree of instability of the energy surface. An analysis of the probability distribution of the Hessian index is therefore relevant for a geometric characterization of the energy landscape in disordered systems. The approach we use here is particularly suitable for this purpose, since it addresses the problem without any a priori assumption on the random matrix ensemble and can be naturally extended to more realistic, non-Gaussian distributions.

cond-mat.stat-mech↗
arXiv1999

A thermal model for adaptive competition in a market

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel non-linear equations for the dynamics of the system.

cond-mat.stat-mech↗
arXiv1999

Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids

We analytically compute the spectrum of the Hessian of the Hamiltonian for a system of N particles interacting via a purely repulsive potential in one dimension. Our approach is valid in the low density regime, where we compute the exact spectrum also in the localized sector. We finally perform a numerical analysis of the localization properties of the eigenfunctions.

cond-mat.stat-mech↗
arXiv1998

Energy distribution of maxima and minima in a one-dimensional random system

We study the energy distribution of maxima and minima of a simple one-dimensional disordered Hamiltonian. We find that in systems with short range correlated disorder there is energy separation between maxima and minima, such that at fixed energy only one kind of stationary points is dominant in number over the other. On the other hand, in the case of systems with long range correlated disorder maxima and minima are completely mixed.

cond-mat.dis-nn↗
arXiv1998

Quenched complexity of the p-spin spherical spin-glass with external magnetic field

We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless-Anderson-Palmer states, performing a quenched computation. We find what is the general connection between this method and the standard static 1-RSB one, formulating a clear mapping between the parameters used in the two different calculations. We also perform a dynamical analysis of the model, by which we confirm the validity of our results.

cond-mat.dis-nn↗
arXiv1997

On the stationary points of the TAP free energy

In the context of the p-spin spherical model, we introduce a method for the computation of the number of stationary points of any nature (minima, saddles, etc.) of the TAP free energy. In doing this we clarify the ambiguities related to the approximations usually adopted in the standard calculations of the number of states in mean field spin glass models.

cond-mat.dis-nn↗
arXiv1997

An investigation of the hidden structure of states in a mean field spin glass model

We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the presence of an exponentially high number of states, each one having a vanishing weight in the thermodynamic limit. Performing a purely entropic computation, based on the TAP equations for this model, we define a constrained complexity which gives the overlap distribution of the states. We find that this distribution is continuous, non-random and highly dependent on the energy range of the considered states. Furthermore, we show which is the geometrical shape of the threshold landscape, giving some insight into the role played by threshold states in the dynamical behaviour of the system.

cond-mat.dis-nn↗
arXiv1996

Structure of metastable states in spin glasses by means of a three replica potential

We introduce a three replica potential useful to examine the structure of metastables states above the static transition temperature, in the spherical p-spin model. Studying the minima of the potential we are able to find which is the distance between the nearest equilibrium and local equilibrium states, obtaining in this way information on the dynamics of the system. Furthermore, the analysis of the potential at the dynamical transition temperature suggests that equilibrium states are not randomly distributed in the phase space.

cond-mat.dis-nn↗