arXiv subjects

M. Marsili

Publications and source records attributed to M. Marsili.

At least 37 records · Page 2Linked to original sources

arXiv2004

Adaptive drivers in a model of urban traffic

We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers' behavioral parameters via numerical simulations and mean-field analytical arguments. We identify a phase transition between a low- and a high-density regime. In the latter, inductive drivers may surprisingly behave worse than randomly selecting drivers.

cond-mat.stat-mech↗

arXiv2003

Statistical mechanics of the majority game

The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield like hamiltonian. On the basis of a replica symmetric calculations, we draw the phase diagram, which contains the analog of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2001

Continuum time limit and stationary states of the Minority Game

We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such equations. In particular, i) we confirm that the stationary state properties are given by the ground state configurations of a disordered (soft) spin system; ii) we derive the full stationary state distribution; iii) we characterize the dependence on initial conditions in the symmetric phase and iv) we clarify the behavior of the system as a function of the learning rate. This leaves us with a complete and coherent picture of the collective behavior of the Minority Game. Strikingly we find that the temperature like parameter which is introduced in the choice behavior of individual agents turns out to play the role, at the collective level, of the inverse of a thermodynamic temperature.

cond-mat.stat-mech↗

arXiv2001

Learning to coordinate in a complex and non-stationary world

We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition as a function of the ratio between the memory $λ$ and the learning rates $Γ$ of the agents. We show that, starting from a random configuration, a dynamic phase transition also exists, which prevents the system from reaching any Nash equilibria. Furthermore, in a non-stationary environment, we show by numerical simulations that agents with infinite memory play worst than others with less memory and that the dynamic transition naturally arises independently from the initial conditions.

cond-mat.stat-mech↗

arXiv2001

Minority Games and stylized facts

The Minority Game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extend this is a reasonable statement, and present minimal modifications that make this model reproduce stylized facts. The resulting model shows that without speculators, prices follow random walks, and that stylized facts disappear if enough speculators take into account their market impact.

cond-mat.stat-mech↗

arXiv2000

From Minority Games to real markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behavior close to what is observed in real markets. In particular we find that i) fat tails and clustered volatility arise at the phase transition point and that ii) the crossover to random walk behavior of prices is a finite size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real market, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different_species_ of traders. This clarifies the nature of the interaction and the particular role played by the various populations.

cond-mat.stat-mech↗

arXiv2000

Trading behavior and excess volatility in toy markets

We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive reactivity of agents. These issues are dealt with in detail in the simple case without public information. We also derive, for the general case, the critical learning rate above which trading behavior leads to turbulent dynamics of the market.

cond-mat.stat-mech↗

arXiv2000

Comment on: Thermal model for Adaptive Competition in a Market

We show that the dynamical equations describing the collective behavior of the model introduced by Cavagna et al. i) are not their Eqs. (5,6) but rather ii) are the same as those of the minority game (MG). As a consequence the analytic solution of the MG presented in [PRL, 84, 1824 (2000)] holds also for this model. Finally we show that iii) the the large temperature behavior of the model is different, due to small simulation times, from that discussed by Cavagna et al.

cond-mat.stat-mech↗

arXiv2000

Data clustering and noise undressing of correlation matrices

We discuss a new approach to data clustering. We find that maximum likelyhood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data. For random, uncorrelated data sets no correlation structure emerges. On the other hand for data sets with a built-in cluster structure, the method is able to detect and recover efficiently that structure. Finally we apply the method to financial time series, where the low temperature behavior reveals a non trivial clustering.

cond-mat.stat-mech↗

arXiv1999

Statistical mechanics of systems with heterogeneous agents: Minority Games

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytic findings.

cond-mat.stat-mech↗

arXiv1999

Scale Invariant Dynamics of Surface Growth

We describe in detail and extend a recently introduced nonperturbative renormalization group (RG) method for surface growth. The scale invariant dynamics which is the key ingredient of the calculation is obtained as the fixed point of a RG transformation relating the representation of the microscopic process at two different coarse-grained scales. We review the RG calculation for systems in the Kardar-Parisi-Zhang universality class and compute the roughness exponent for the strong coupling phase in dimensions from 1 to 9. Discussions of the approximations involved and possible improvements are also presented. Moreover, very strong evidence of the absence of a finite upper critical dimension for KPZ growth is presented. Finally, we apply the method to the linear Edwards-Wilkinson dynamics where we reproduce the known exact results, proving the ability of the method to capture qualitatively different behaviors.

cond-mat.stat-mech↗

arXiv1998

Generalized Dielectric Breakdown Model

We propose a generalized version of the Dielectric Breakdown Model (DBM) for generic breakdown processes. It interpolates between the standard DBM and its analog with quenched disorder, as a temperature like parameter is varied. The physics of other well known fractal growth phenomena as Invasion Percolation and the Eden model are also recovered for some particular parameter values. The competition between different growing mechanisms leads to new non-trivial effects and allows us to better describe real growth phenomena. Detailed numerical and theoretical analysis are performed to study the interplay between the elementary mechanisms. In particular, we observe a continuously changing fractal dimension as temperature is varied, and report an evidence of a novel phase transition at zero temperature in absence of an external driving field; the temperature acts as a relevant parameter for the ``self-organized'' invasion percolation fixed point. This permits us to obtain new insight into the connections between self-organization and standard phase transitions.

cond-mat↗

arXiv1998

High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent $α$ decays not faster than $α\sim 1/d$ for large $d$. This implies the absence of a finite upper critical dimension.

cond-mat.stat-mech↗

arXiv1998

Non perturbative renormalization group approach to surface growth

We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties of the KPZ strong coupling fixed point, which is not accessible to standard perturbative field theory approaches. Using this method, and with the aid of small Monte Carlo calculations for systems of linear size 2 and 4, we calculate the roughness exponent in dimensions up to d=8. The results agree with the known numerical values with good accuracy. Furthermore, the method permits us to predict the absence of an upper critical dimension for KPZ contrarily to recent claims. The RG scheme is applied to other growth models in different universality classes and reproduces very well all the observed phenomenology and numerical results. Intended as a sort of finite size scaling method, the new scheme may simplify in some cases from a computational point of view the calculation of scaling exponents of growth processes.

cond-mat↗

arXiv1998

Non-perturbative renormalization of the KPZ growth dynamics

We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic (self-affine) scaling are overcome with an indirect functional renormalization. The roughness exponent $α$ is computed for dimensions $d=1$ to 8 and it results to be in very good agreement with the available simulations. No evidence is found for an upper critical dimension. We discuss how the present approach can be extended to other self-affine problems.

cond-mat.stat-mech↗

arXiv1998

On the High-dimensional Bak-Sneppen model

We report on extensive numerical simulations on the Bak-Sneppen model in high dimensions. We uncover a very rich behavior as a function of dimensionality. For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process becomes transient. Finally the exponents reach their mean field values for d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.

cond-mat.stat-mech↗

arXiv1997

A Prototype Model of Stock Exchange

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate his assets by speculating on the price's fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets.

cond-mat.stat-mech↗

arXiv1997

Scaling Behavior in the Stable Marriage Problem

We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best solution, but reasonably close to it. All the stable solutions form a special sub-set of the meta-stable states, obeying interesting scaling laws. Both numerical and analytical tools are used to derive our results.

cond-mat↗