scholarly journals Entropic repulsion on a rarefied wall

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
L. R. G. Fontes ◽  
M. Vachkovskaia ◽  
A. Yambartsev
Keyword(s):  
Random Walk ◽  
Entropic Repulsion ◽  
Random Surface ◽  
International Audience ◽  
The Mean ◽  
Number Of Visits

International audience We consider the motion of a discrete d-dimensional random surface interacting by exclusion with a rarefied wall. The dynamics is given by the serial harness process. We prove that the process delocalizes iff the mean number of visits to the set of sites where the wall is present by some random walk is infinite. In case where there is a delocalization, bounds on its speed are obtained.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

scholarly journals The Limiting Distribution for the Number of Symbol Comparisons Used by QuickSort is Nondegenerate (Extended Abstract)

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Patrick Bindjeme ◽  
james Allen fill
Keyword(s):  
Large Class ◽  
Continuous Time ◽  
Random Variable ◽  
Limiting Distribution ◽  
International Audience ◽  
The Mean

International audience In a continuous-time setting, Fill (2012) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by $\texttt{QuickSort}$, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable $Y$—not even that it is nondegenerate. We establish the nondegeneracy of $Y$. The proof is perhaps surprisingly difficult.

scholarly journals Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Ho-Kwok Dai ◽  
Hung-Chi Su
Keyword(s):  
Random Walk ◽  
Dimensional Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Order Curve ◽  
Cluster Distance ◽  
The Mean ◽  
Curve Family

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.

Series expansions for the all-time maximum of α-stable random walks

2016 ◽  
Vol 48 (3) ◽  
pp. 744-767
Author(s):  
Clifford Hurvich ◽  
Josh Reed
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Queueing Theory ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Series Expansions ◽  
Stable Random Variables ◽  
The Mean ◽  
The Stability

AbstractWe study random walks whose increments are α-stable distributions with shape parameter 1<α<2. Specifically, assuming a mean increment size which is negative, we provide series expansions in terms of the mean increment size for the probability that the all-time maximum of an α-stable random walk is equal to 0 and, in the totally skewed-to-the-left case of skewness parameter β=-1, for the expected value of the all-time maximum of an α-stable random walk. Our series expansions generalize previous results for Gaussian random walks. Key ingredients in our proofs are Spitzer's identity for random walks, the stability property of α-stable random variables, and Zolotarev's integral representation for the cumulative distribution function of an α-stable random variable. We also discuss an application of our results to a problem arising in queueing theory.

scholarly journals On sojourn times at particular gene frequencies

1975 ◽  
Vol 25 (2) ◽  
pp. 89-94 ◽  
Author(s):  
Edward Pollak ◽  
Barry C. Arnold
Keyword(s):  
Markov Chains ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Finite Population ◽  
Diffusion Method ◽  
Gene Frequencies ◽  
Sojourn Times ◽  
The Mean ◽  
Number Of Visits ◽  
Finite Markov Chains

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

scholarly journals Can Mean Helicity Fluctuations Explain the Variability of the Solar Cycle ?

1993 ◽  
Vol 157 ◽  
pp. 71-75
Author(s):  
P. Hoyng
Keyword(s):  
Random Walk ◽  
Solar Cycle ◽  
Phase Shift ◽  
Correlated Random Walk ◽  
The Mean ◽  
Dynamo Wave

I consider the effect of rapid fluctuations in the mean helicity on a plane dynamo wave in the αω-approximation and in the weak forcing limit. The phase shift and the logarithmic amplitude of the wave exhibit a correlated random walk, so that weaker (stronger) cycles last longer (shorter). The solar cycle data follow this prediction rather well. Mean helicity fluctuations are concluded to be an important source of solar cycle variability.

scholarly journals Impact of Health Insurance on Health Care Utilisation and Out-of-Pocket Health Expenditure in Vietnam

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Thu Thuong ◽  
Tran Quang Huy ◽  
Do Anh Tai ◽  
Tran Nhuan Kien
Keyword(s):  
Health Care ◽  
Health Insurance ◽  
Health Care Providers ◽  
Health Care Utilisation ◽  
Health Coverage ◽  
Care Providers ◽  
Care Utilisation ◽  
The Mean ◽  
Number Of Visits ◽  
Universal Health

Background. In recent years, health insurance (HI) has been chosen by many low- and middle-income countries to obtain an important health policy target—universal health coverage. Vietnam has recently introduced the Revised Health Insurance Law, and the effects of the voluntary health insurance (VHI) and heavily subsidised health insurance (HSHI) programmes have not yet been analysed. Therefore, this study is aimed at examining the impact of these HI programmes on the utilisation of health care services and out-of-pocket health expenditure (OOP) in general and across different health care providers in particular. Methods. Using the two waves of Vietnam Household Living Standard Surveys 2014 and 2016 and the difference-in-difference method, the impacts of VHI and HSHI on health care utilisation and OOP in Vietnam were estimated. Results. For both the VHI and HSHI groups, we found that HI increased the probability of seeking outpatient care, the mean number of outpatient visits, the total number of visits, and the mean number of visits at the district level of health care providers in the last 12 months. However, there was no evidence that the HSHI programmes increased the mean number of inpatient visits and the number of visits at the provincial hospital. We also found that while the VHI programme reduced OOP for both outpatient and inpatient care, the HSHI scheme did not result in a reduction in OOP for hospitalisation, although HI lowered the total OOP. Similarly, we found that for both groups, HI reduced OOP when the insured visited district and provincial hospitals. However, the statistically significant impact was not demonstrated when the enrolees of HSHI programmes visited provincial hospitals. Conclusion. The study offers evidence that the Vietnamese HI scheme increased health care service utilisation and decreased OOP for the participants of the VHI and HSHI programmes. Therefore, the government should continue to consider improving the HI system as a strategy to achieve universal health coverage.

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