1,092 research outputs found
Microscopic models of financial markets
This review deals with several microscopic models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation approaches in financial economics, we first give a summary of the Donangelo-Sneppen model of monetary exchange and compare it with related models in economics literature. Our selective review then outlines the main ingredients of some influential early models of multi-agent dynamics in financial markets (Kim-Markowitz, Levy-Levy-Solomon). As will be seen, these contributions draw their inspiration from the complex appearance of investors' interactions in real-life markets. Their main aim is to reproduce (and, thereby, provide possible explanations) for the spectacular bubbles and crashes seen in certain historical episodes, but they lack (like almost all the work before 1998 or so) a perspective in terms of the universal statistical features of financial time series. In fact, awareness of a set of such regularities (power-law tails of the distribution of returns, temporal scaling of volatility) only gradually appeared over the nineties. With the more precise description of the formerly relatively vague characteristics (e.g. moving from the notion of fat tails to the more concrete one of a power-law with index around three), it became clear that financial markets dynamics give rise to some kind of universal scaling laws. Showing similarities with scaling laws for other systems with many interacting subunits, an exploration of financial markets as multi-agent systems appeared to be a natural consequence. This topic was pursued by quite a number of contributions appearing in both the physics and economics literature since the late nineties. From the wealth of different flavors of multi-agent models that have appeared by now, we discuss the Cont-Bouchaud, Solomon-Levy-Huang and Lux-Marchesi models. Open research questions are discussed in our concluding section. --
Percolation quantum phase transitions in diluted magnets
We show that the interplay of geometric criticality and quantum fluctuations
leads to a novel universality class for the percolation quantum phase
transition in diluted magnets. All critical exponents involving dynamical
correlations are different from the classical percolation values, but in two
dimensions they can nonetheless be determined exactly. We develop a complete
scaling theory of this transition, and we relate it to recent experiments in
LaCu(Zn,Mg)O. Our results are also relevant for
disordered interacting boson systems.Comment: 4 pages, 3 eps figures, final version, as publishe
Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
The long-time behavior of transport coefficients in a model for spatially
heterogeneous media in two and three dimensions is investigated by Molecular
Dynamics simulations. The behavior of the velocity auto-correlation function is
rationalized in terms of a competition of the critical relaxation due to the
underlying percolation transition and the hydrodynamic power-law anomalies. In
two dimensions and in the absence of a diffusive mode, another power law
anomaly due to trapping is found with an exponent -3 instead of -2. Further,
the logarithmic divergence of the Burnett coefficient is corroborated in the
dilute limit; at finite density, however, it is dominated by stronger
divergences.Comment: Full-length paragraph added that exemplifies the relevance for dense
fluids and makes a connection to recently observed, novel long-time tails in
a hard-sphere flui
Non-equilibrium multi-scale analysis and coexistence in competing first passage percolation
The main contribution of this paper is the development of a novel approach to
multi-scale analysis that we believe can be used to analyse processes with
non-equilibrium dynamics. Our approach will be referred to as \emph{multi-scale
analysis with non-equilibrium feedback} and will be used to analyse a natural
random growth process with competition on called \emph{first
passage percolation in a hostile environment} that consists of two first
passage percolation processes and that compete for the
occupancy of sites. Initially, occupies the origin and spreads through
the edges of at rate 1, while is initialised at
sites called \emph{seeds} that are distributed according to a product of
Bernoulli measures of parameter , where a seed remains dormant until
or attempts to occupy it before then spreading through
the edges of at rate . Particularly challenging
aspects of FPPHE are its non-equilibrium dynamics and its lack of monotonicity
(for instance, adding seeds could be benefitial to instead of
); such characteristics, for example, prevent the application of a
more standard multi-scale analysis. As a consequence of our main result for
FPPHE, we establish a coexistence phase for the model for , answering
an open question in \cite{sidoravicius2019multi}. This exhibits a rare
situation where a natural random competition model on observes
coexistence for processes with \emph{different} speeds. Moreover, we are able
to establish the stronger result that and can both
occupy a \emph{positive density} of sites with positive probability, which is
in stark contrast with other competition processes.Comment: 48 pages, revised version with minor correction
Coexistence in competing first passage percolation with conversion
We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are initially vacant. Once a site is occupied by type 1, it converts to type 2 at rate ρ >0. Sites occupied by type 2 then spread at rate λ>0 through vacant sites and sites occupied by type 1, whereas type 1 can only spread through vacant sites. If the set of sites occupied by type 1 is nonempty at all times, we say type 1 survives. In the case of a regular d-ary tree for d ≥ 3, we show type 1 can survive when it is slower than type 2, provided ρ is small enough. This is in contrast to when the underlying graph is Zd , where for any ρ >0, type 1 dies out almost surely if λ > λ ' for some λ ' < 1.</p
Percolation transition and dissipation in quantum Ising magnets
We study the effects of dissipation on a randomly diluted transverse-field
Ising magnet close to the percolation threshold. For weak transverse fields, a
novel percolation quantum phase transition separates a superparamagnetic
cluster phase from an inhomogeneously ordered ferromagnetic phase. The
properties of this transition are dominated by large frozen and slowly
fluctuating percolation clusters. This leads to a discontinuous
magnetization-field curve and exotic hysteresis phenomena as well as highly
singular behavior of magnetic susceptibility and specific heat. We compare our
results to the smeared transition in generic dissipative random quantum Ising
magnets. We also discuss the relation to metallic quantum magnets and other
experimental realizations.Comment: 4 pages, 2 eps figures, final version as publishe
Structural Properties of Two-Dimensional Polymers
We present structural properties of two-dimensional polymers as far as they
can be described by percolation theory. The percolation threshold, critical
exponents and fractal dimensions of clusters are determined by computer
simulation and compared to the results of percolation theory. We also describe
the dependence of the typical cluster structures on the reaction rate.Comment: 7 pages, LaTeX with RevTeX and epsf styles and PostScript figures
included (uuencoded shell archive), TVP-93051
Dissipation effects in percolating quantum Ising magnets
We study the effects of dissipation on a randomly dilute transverse-field
Ising magnet at and close to the percolation threshold. For weak transverse
fields, a novel percolation quantum phase transition separates a
super-paramagnetic cluster phase from an inhomogeneously ordered ferromagnetic
phase. The properties of this transition are dominated by large frozen and
slowly fluctuating percolation clusters. Implementing numerically a
strong-disorder real space renormalization group technique, we compute the
low-energy density of states which is found to be in good agreement with the
analytical prediction.Comment: 2 pages, 1 eps figure, final version as publishe
Absorbing-state phase transitions on percolating lattices
We study nonequilibrium phase transitions of reaction-diffusion systems
defined on randomly diluted lattices, focusing on the transition across the
lattice percolation threshold. To develop a theory for this transition, we
combine classical percolation theory with the properties of the supercritical
nonequilibrium system on a finite-size cluster. In the case of the contact
process, the interplay between geometric criticality due to percolation and
dynamical fluctuations of the nonequilibrium system leads to a new universality
class. The critical point is characterized by ultraslow activated dynamical
scaling and accompanied by strong Griffiths singularities. To confirm the
universality of this exotic scaling scenario we also study the generalized
contact process with several (symmetric) absorbing states, and we support our
theory by extensive Monte-Carlo simulations.Comment: 11 pages, 10 eps figures included, final version as publishe
Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation
We investigate the influence of sub-Ohmic dissipation on randomly diluted
quantum Ising and rotor models. The dissipation causes the quantum dynamics of
sufficiently large percolation clusters to freeze completely. As a result, the
zero-temperature quantum phase transition across the lattice percolation
threshold separates an unusual super-paramagnetic cluster phase from an
inhomogeneous ferromagnetic phase. We determine the low-temperature
thermodynamic behavior in both phases which is dominated by large frozen and
slowly fluctuating percolation clusters. We relate our results to the smeared
transition scenario for disordered quantum phase transitions, and we compare
the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.Comment: 9 pages, 2 figure
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