Search results for "Random walk"
showing 10 items of 132 documents
Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement
2022
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting L\'{e}vy process…
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
Diffusive Behavior and the Modeling of Characteristic Times in Limit Order Executions
2007
We present a study of the order book data of the London Stock Exchange for five highly liquid stocks traded during the calendar year 2002. Specifically, we study the first passage time of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones. We find that the distribution of the first passage time decays asymptotically in time as a power law with an exponent L_FPT ~ 1.5. The median of the same quantity scales as Delta^1.6, which is different from the Delta^2 behavior expected for Brownian motion. The quantities TTF, and TTC are also asymptotically power law distributed with exponen…
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
1993
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short ini…
Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition.
2012
The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the $z$-ensemble, the displacement $z$ of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a contro…
Reply to "comment on 'Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions' ".
2002
As is well known, a wide class of physical problems, including the kinetics of heterogeneous catalytic reactions, is traditionally described in terms of the master equations ~ME!. The definition of ME allows us not only to perform Monte Carlo ~MC! simulations, but also to develop at the same time appropriate analytical methods @mean field~MF!, cluster approximations, etc. #@ 1#. ME is formally defined when all possible states of a system and the transition rates between these states are specified. This is enough to define only the transition rates K(i! j ) for such elementary processes as particle adsorption, desorption, diffusion, reaction, etc., from the initial state i to the final state…
Phase separation of symmetric polymer mixtures in a common good solvent in the semidilute concentration regime
1994
Monte Carlo simulations of lattice models of binary (AB) symmetric polymer mixtures (chain lengthsN A=N B=N) in a common good solvent are carried out and the phase diagrams and critical properties of the unmixing transitions are estimated and interpreted in terms of recent theories. Polymers are modeled by self-avoiding walks of lengthN=16, 32 and 64 on the simple cubic lattice. Data for vacancy concentrations of φV=0.6, 0.8 and 0.85 are analyzed. It is shown that forN=16, φV=0.85 no phase separation occurs, down to the lowest temperature, while forN=32, φV=0.85 still phase separation occurs but no longer is complete. Our results are compatible with a scaling theory based on a “renormalizat…
A solution to the stochastic point location problem in metalevel nonstationary environments.
2008
This paper reports the first known solution to the stochastic point location (SPL) problem when the environment is nonstationary. The SPL problem involves a general learning problem in which the learning mechanism (which could be a robot, a learning automaton, or, in general, an algorithm) attempts to learn a "parameter," for example, lambda*, within a closed interval. However, unlike the earlier reported results, we consider the scenario when the learning is to be done in a nonstationary setting. For each guess, the environment essentially informs the mechanism, possibly erroneously (i.e., with probability p), which way it should move to reach the unknown point. Unlike the results availabl…
Conclusions: Take-Home Messages
2014
In this chapter, which mainly consists of headlines, the take-home messages of the lecture notes are presented.
Combining finite learning automata with GSAT for the satisfiability problem
2010
A large number of problems that occur in knowledge-representation, learning, very large scale integration technology (VLSI-design), and other areas of artificial intelligence, are essentially satisfiability problems. The satisfiability problem refers to the task of finding a satisfying assignment that makes a Boolean expression evaluate to True. The growing need for more efficient and scalable algorithms has led to the development of a large number of SAT solvers. This paper reports the first approach that combines finite learning automata with the greedy satisfiability algorithm (GSAT). In brief, we introduce a new algorithm that integrates finite learning automata and traditional GSAT use…