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Добірка наукової літератури з теми "Symmetric random walk"

Автор: Grafiati

Опубліковано: 15 грудня 2023

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Статті в журналах з теми "Symmetric random walk"

1

LI, KEQIN. "PERFORMANCE ANALYSIS AND EVALUATION OF RANDOM WALK ALGORITHMS ON WIRELESS NETWORKS." International Journal of Foundations of Computer Science 23, no. 04 (2012): 779–802. http://dx.doi.org/10.1142/s0129054112400369.

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Анотація:

We propose a model of dynamically evolving random networks and give an analytical result of the cover time of the simple random walk algorithm on a dynamic random symmetric planar point graph. Our dynamic network model considers random node distribution and random node mobility. We analyze the cover time of the parallel random walk algorithm on a complete network and show by numerical data that k parallel random walks reduce the cover time by almost a factor of k. We present simulation results for four random walk algorithms on random asymmetric planar point graphs. These algorithms include the simple random walk algorithm, the intelligent random walk algorithm, the parallel random walk algorithm, and the parallel intelligent random walk algorithm. Our random network model considers random node distribution and random battery transmission power. Performance measures include normalized cover time, probability distribution of the length of random walks, and load distribution.

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2

Zygmunt, Marcin J. "Non symmetric random walk on infinite graph." Opuscula Mathematica 31, no. 4 (2011): 669. http://dx.doi.org/10.7494/opmath.2011.31.4.669.

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3

Godrèche, Claude, and Jean-Marc Luck. "Survival probability of random walks and Lévy flights with stochastic resetting." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 7 (2022): 073201. http://dx.doi.org/10.1088/1742-5468/ac7a2a.

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Анотація:

Abstract We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up to time n. For continuous symmetric distributions of step lengths with either finite (random walks) or infinite variance (Lévy flights), this probability can be expressed in terms of the survival probability of the walk without resetting, given by Sparre Andersen theory. It is therefore universal, i.e. independent of the step length distribution. We analyze this survival probability at depth, deriving both exact results at finite times and asymptotic late-time results. We also investigate the case where the step length distribution is symmetric but not continuous, focusing our attention onto arithmetic distributions generating random walks on the lattice of integers. We investigate in detail the example of the simple Polya walk and propose an algebraic approach for lattice walks with a larger range.

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4

YANG, ZHIHUI. "LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS." Stochastics and Dynamics 07, no. 01 (2007): 75–89. http://dx.doi.org/10.1142/s0219493707001950.

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Анотація:

Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.

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5

Telcs, András, and Nicholas C. Wormald. "Branching and tree indexed random walks on fractals." Journal of Applied Probability 36, no. 4 (1999): 999–1011. http://dx.doi.org/10.1239/jap/1032374750.

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Анотація:

This paper deals with the recurrence of branching random walks on polynomially growing graphs. Amongst other things, we demonstrate the strong recurrence of tree indexed random walks determined by the resistance properties of spherically symmetric graphs. Several branching walk models are considered to show how the branching mechanism influences the recurrence behaviour.

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6

Telcs, András, and Nicholas C. Wormald. "Branching and tree indexed random walks on fractals." Journal of Applied Probability 36, no. 04 (1999): 999–1011. http://dx.doi.org/10.1017/s0021900200017812.

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Анотація:

This paper deals with the recurrence of branching random walks on polynomially growing graphs. Amongst other things, we demonstrate the strong recurrence of tree indexed random walks determined by the resistance properties of spherically symmetric graphs. Several branching walk models are considered to show how the branching mechanism influences the recurrence behaviour.

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7

Hilário, Marcelo R., Daniel Kious, and Augusto Teixeira. "Random Walk on the Simple Symmetric Exclusion Process." Communications in Mathematical Physics 379, no. 1 (2020): 61–101. http://dx.doi.org/10.1007/s00220-020-03833-x.

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Анотація:

Abstract We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole, so that its asymptotic behavior is expected to depend on the density $$\rho \in [0, 1]$$ ρ ∈ [ 0 , 1 ] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities $$\rho $$ ρ except for at most two values $$\rho _-, \rho _+ \in [0, 1]$$ ρ - , ρ + ∈ [ 0 , 1 ] . The asymptotic speed we obtain in our LLN is a monotone function of $$\rho $$ ρ . Also, $$\rho _-$$ ρ - and $$\rho _+$$ ρ + are characterized as the two points at which the speed may jump to (or from) zero. Furthermore, for all the values of densities where the random walk experiences a non-zero speed, we can prove that it satisfies a functional central limit theorem (CLT). For the special case in which the density is 1/2 and the jump distribution on an empty site and on an occupied site are symmetric to each other, we prove a LLN with zero limiting speed. We also prove similar LLN and CLT results for a different environment, given by a family of independent simple symmetric random walks in equilibrium.

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8

Fujita, Takahiko. "A random walk analogue of Lévy’s Theorem." Studia Scientiarum Mathematicarum Hungarica 45, no. 2 (2008): 223–33. http://dx.doi.org/10.1556/sscmath.45.2008.2.50.

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Анотація:

In this paper we will give a simple symmetric random walk analogue of Lévy’s Theorem. We will give a new definition of a local time of the simple symmetric random walk. We apply a discrete Itô formula to some absolute value like function to obtain a discrete Tanaka formula. Results in this paper rely upon a discrete Skorokhod reflection argument. This random walk analogue of Lévy’s theorem was already obtained by G. Simons ([14]) but it is still worth noting because we will use a discrete stochastic analysis to obtain it and this method is applicable to other research. We note some connection with previous results by Csáki, Révész, Csörgő and Szabados. Finally we observe that the discrete Lévy transformation in the present version is not ergodic. Lastly we give a Lévy-type theorem for simple nonsymmetric random walk using a discrete bang-bang process.

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9

ISHIMURA, N., and N. YOSHIDA. "ON THE CONVERGENCE OF DISCRETE PROCESSES WITH MULTIPLE INDEPENDENT VARIABLES." ANZIAM Journal 58, no. 3-4 (2017): 379–85. http://dx.doi.org/10.1017/s1446181116000389.

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Анотація:

We discuss discrete stochastic processes with two independent variables: one is the standard symmetric random walk, and the other is the Poisson process. Convergence of discrete stochastic processes is analysed, such that the symmetric random walk tends to the standard Brownian motion. We show that a discrete analogue of Ito’s formula converges to the corresponding continuous formula.

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10

Fang, Xiao, Han L. Gan, Susan Holmes, et al. "Arcsine laws for random walks generated from random permutations with applications to genomics." Journal of Applied Probability 58, no. 4 (2021): 851–67. http://dx.doi.org/10.1017/jpr.2021.14.

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Анотація:

AbstractA classical result for the simple symmetric random walk with 2n steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge when scaled to the arcsine law. Motivated by applications in genomics, we study the distributions of these statistics for the non-Markovian random walk generated from the ascents and descents of a uniform random permutation and a Mallows(q) permutation and show that they have the same asymptotic distributions as for the simple random walk. We also give an unexpected conjecture, along with numerical evidence and a partial proof in special cases, for the result that the number of steps above the origin by step 2n for the uniform permutation generated walk has exactly the same discrete arcsine distribution as for the simple random walk, even though the other statistics for these walks have very different laws. We also give explicit error bounds to the limit theorems using Stein’s method for the arcsine distribution, as well as functional central limit theorems and a strong embedding of the Mallows(q) permutation which is of independent interest.

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