scholarly journals A Hybrid Analog-Digital Parameter Optimizer for ASTRAC II

SIMULATION ◽  
1965 ◽  
Vol 4 (6) ◽  
pp. 399-411 ◽  
Author(s):  
Baker Adams Mitchell
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Performance Measure ◽  
Random Perturbations ◽  
Parameter Perturbation ◽  
Step Size ◽  
Digital To Analog Converters ◽  
Different Types ◽  
Nominal Parameter ◽  
System Performance Measure

A new automatic multiparameter optimizer for iter ative differential analyzers employs sequential ran dom parameter perturbation. The nominal parameter point changes whenever the random perturbations improve the system performance measure. Binary counters operate simple digital-to-analog converters to implement parameter storage, multiplication, and step-size changes. All-digital logic yields different types of random perturbations, viz., simple random walk, random walk with reflecting or absorbing bar riers, and various types of correlation over successive perturbations.

scholarly journals A simple random walk model explains the disruption process of hierarchical, Eccentric three-body systems

2020 ◽  
Vol 498 (1) ◽  
pp. 665-673
Author(s):  
Jonathan Mushkin ◽  
Boaz Katz
Keyword(s):  
Random Walk ◽  
Initial Conditions ◽  
Simple Random Walk ◽  
Survival Times ◽  
Step Size ◽  
Orbital Parameters ◽  
Unstable Set ◽  
Three Body ◽  
First Time ◽  
Comparable Mass

ABSTRACT We study the disruption process of hierarchical three-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with three-body numerical integrations, we show that the evolution and disruption of such systems can be statistically described as a simple random walk process in the outer orbit’s energy, where the energy exchange per pericenter passage (step size) is calculated from the initial conditions. In our derivation of the step size, we use previous analytic results for parabolic encounters, and average over the (Kozai–Lidov) oscillations in orbital parameters, which are faster then the energy diffusion time-scale. While similar random walk models were studied before, this work differs in two manners: (a) this is the first time that the Kozai–Lidov averaged step size is derived from first principles and demonstrated to reproduce the statistical evolution of numerical ensembles without fitting parameters, and (b) it provides a characteristic lifetime, instead of answering the binary question (stable/unstable), set by case-specific criteria.

scholarly journals The Speed of Simple Random Walk and Anchored Expansion on Percolation Clusters: an Overview

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Dayue Chen ◽  
Yuval Peres
Keyword(s):  
Random Walk ◽  
Percolation Cluster ◽  
Simple Random Walk ◽  
Random Perturbations ◽  
Exponential Tail ◽  
Infinite Cluster ◽  
Lamplighter Group ◽  
Percolation Clusters ◽  
Percolation Parameter ◽  
International Audience

International audience Benjamini, Lyons and Schramm (1999) considered properties of an infinite graph $G$, and the simple random walk on it, that are preserved by random perturbations. To address problems raised by those authors, we study simple random walk on the infinite percolation cluster in Cayley graphs of certain amenable groups known as "lamplighter groups''.We prove that zero speed for random walk on a lamplighter group implies zero speed for random walk on an infinite cluster, for any supercritical percolation parameter $p$. For $p$ large enough, we also establish the converse. We prove that if $G$ has a positive anchored expansion constant then so does every infinite cluster of independent percolation with parameter $p$ sufficiently close to 1; We also show that positivity of the anchored expansion constant is preserved under a random stretch if, and only if, the stretching law has an exponential tail.

The size of the region occupied by one type in an invasion process

1976 ◽  
Vol 13 (02) ◽  
pp. 355-356 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Rectangular Lattice ◽  
Invasion Process

Particles are situated on a rectangular lattice and proceed to invade each other's territory. When they are equally competitive this creates larger and larger blocks of one type as time goes by. It is shown that the expected size of such blocks is equal to the expected range of a simple random walk.

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

A Simple Random Walk Model for Dairy Cow Calving Time Prediction

2021 ◽  
Author(s):  
Thi Thi Zin ◽  
Pyke Tin ◽  
Pann Thinzar Seint ◽  
Kosuke Sumi ◽  
Ikuo Kobayashi ◽  
...  
Keyword(s):  
Random Walk ◽  
Dairy Cow ◽  
Simple Random Walk ◽  
Random Walk Model ◽  
Time Prediction

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

On the number of times where a simple random walk reaches its maximum

1992 ◽  
Vol 29 (02) ◽  
pp. 305-312 ◽  
Author(s):  
W. Katzenbeisser ◽  
W. Panny
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Probability And Statistics

Let Qn denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important role in probability and statistics. In this paper the distribution and the moments of Qn , are considered and their asymptotic behavior is studied.

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