A simple random walk on parallel axes moving at different rates

1975 ◽  
Vol 12 (3) ◽  
pp. 466-476 ◽  
Author(s):  
V. Barnett
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Time Instant ◽  
Packed Columns ◽  
The Other ◽  
End Points ◽  
Previous Time ◽  
The Right

Prompted by a rivulet model for the flow of liquid through packed columns we consider a simple random walk on parallel axes moving at different rates. A particle may make one of three transitions at each time instant: to the right or to the left on the axis it was on at the previous time instant, or across to the other axis. Results are obtained for the unrestricted walk, and for the walk with absorbing, or reflecting, end-points.

A simple random walk on parallel axes moving at different rates

1975 ◽  
Vol 12 (03) ◽  
pp. 466-476
Author(s):  
V. Barnett
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Time Instant ◽  
Packed Columns ◽  
The Other ◽  
End Points ◽  
Previous Time ◽  
The Right

Prompted by a rivulet model for the flow of liquid through packed columns we consider a simple random walk on parallel axes moving at different rates. A particle may make one of three transitions at each time instant: to the right or to the left on the axis it was on at the previous time instant, or across to the other axis. Results are obtained for the unrestricted walk, and for the walk with absorbing, or reflecting, end-points.

The fundamental matrix for a certain random walk

1999 ◽  
Vol 36 (02) ◽  
pp. 320-333
Author(s):  
Howard M. Taylor
Keyword(s):  
Random Walk ◽  
Green Function ◽  
Explicit Formula ◽  
Fundamental Matrix ◽  
Simple Random Walk ◽  
Limiting Behavior ◽  
Point Of Entry ◽  
Discrete Lattices ◽  
The Green Function ◽  
The Right

Consider the random walk {Sn} whose summands have the distributionP(X=0) = 1-(2/π), andP(X= ±n) = 2/[π(4n2−1)], forn≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean timexkfor the random walk starting fromS0=kto exit the interval. The explicit formula yields the limiting behavior ofxkasN→ ∞ withkfixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By lettingN→ ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting fromk= 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

scholarly journals Nonhomogeneous random walks systems on ℤ

2010 ◽  
Vol 47 (02) ◽  
pp. 562-571
Author(s):  
Elcio Lebensztayn ◽  
Fábio Prates Machado ◽  
Mauricio Zuluaga Martinez
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Nearest Neighbor ◽  
The Other ◽  
Active Particle ◽  
Positive Probability ◽  
Small Probability ◽  
Active Particles ◽  
Other Hand ◽  
The Right

We consider a random walks system on ℤ in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on ℤ, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to 1 but not fast enough.

scholarly journals Nonhomogeneous random walks systems on ℤ

2010 ◽  
Vol 47 (2) ◽  
pp. 562-571 ◽  
Author(s):  
Elcio Lebensztayn ◽  
Fábio Prates Machado ◽  
Mauricio Zuluaga Martinez
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Nearest Neighbor ◽  
The Other ◽  
Active Particle ◽  
Positive Probability ◽  
Small Probability ◽  
Active Particles ◽  
Other Hand ◽  
The Right

We consider a random walks system on ℤ in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on ℤ, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to 1 but not fast enough.

The fundamental matrix for a certain random walk

1999 ◽  
Vol 36 (2) ◽  
pp. 320-333 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Random Walk ◽  
Green Function ◽  
Explicit Formula ◽  
Fundamental Matrix ◽  
Simple Random Walk ◽  
Limiting Behavior ◽  
Point Of Entry ◽  
Discrete Lattices ◽  
The Green Function ◽  
The Right

Consider the random walk {Sn} whose summands have the distribution P(X=0) = 1-(2/π), and P(X = ± n) = 2/[π(4n2−1)], for n ≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean time xk for the random walk starting from S0 = k to exit the interval. The explicit formula yields the limiting behavior of xk as N → ∞ with k fixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By letting N → ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting from k = 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

scholarly journals Optimal Bounds for the Variance of Self-Intersection Local Times

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
George Deligiannidis ◽  
Sergey Utev
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Simple Random Walk ◽  
The Self ◽  
The Other ◽  
Local Times ◽  
Intersection Local Time ◽  
Moment Conditions ◽  
Symmetric Random Walk ◽  
Optimal Bounds

For a Zd-valued random walk (Sn)n∈N0, let l(n,x) be its local time at the site x∈Zd. For α∈N, define the α-fold self-intersection local time as Ln(α)≔∑xl(n,x)α. Also let LnSRW(α) be the corresponding quantities for the simple random walk in Zd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely d-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, var(Ln(α))=O(var⁡(LnSRW(α))). In particular, for any genuinely d-dimensional random walk, with d≥4, we have var⁡(Ln(α))=O(n). On the other hand, in dimensions d≤3 we show that if the behaviour resembles that of simple random walk, in the sense that lim infn→∞var⁡Lnα/var⁡(LnSRW(α))>0, then the increments of the random walk must have zero mean and finite second moment.

Assessment of knowledge of oral health hygiene among coastal guards in the port trust of south Tamil Nadu - A public health awareness survey

2020 ◽  
Vol 11 (SPL3) ◽  
pp. 1861-1868
Author(s):  
Bianca Princeton ◽  
Abilasha R ◽  
Preetha S
Keyword(s):  
Lung Cancer ◽  
Oral Health ◽  
Oral Hygiene ◽  
Tamil Nadu ◽  
Asbestos Exposure ◽  
The Other ◽  
Oral Manifestations ◽  
Illegal Activities ◽  
The Right ◽  
Oral Hygiene Habits

Oral hygiene is defined as the practice of keeping the mouth clean and healthy, by brushing and flossing to prevent the occurrence of any gum diseases like periodontitis or gingivitis. The main aim of oral health hygiene is to prevent the buildup of plaque, which is defined as a sticky film of bacteria and food formed on the teeth. The coastal guard is an official who is employed to watch the sea near a coast for ships that are in danger or involved with illegal activities. Coastal guards have high possibilities of being affected by mesothelioma or lung cancer due to asbestos exposure. So, a questionnaire consisting of 20 questions was created and circulated among a hundred participants who were coastal guards, through Google forms. The responses were recorded and tabulated in the form of bar graphs. Out of a hundred participants, 52.4% were not aware of the fact that coastal guards have high chances of developing lung cancer and Mesothelioma. 53.7% were aware of the other oral manifestations of lung cancer other than bleeding gums. Majority of the coastal guards feel that they are given enough information about dental hygiene protocols. Hence, to conclude, oral hygiene habits have to be elaborated using various tools in the right manner to ensure better health of teeth and gums.

JUAL BELI TANAH YANG DILAKUKAN TANPA AKTA PPAT

2018 ◽  
Vol 4 (1) ◽  
pp. 89-107
Author(s):  
Cheri Bayuni Budjang
Keyword(s):  
Everyday Life ◽  
Government Regulation ◽  
Land Rights ◽  
The Other ◽  
Legal Certainty ◽  
Land Registration ◽  
The Future ◽  
The Right ◽  
Laws And Regulations

Buying and selling is a way to transfer land rights according to the provisions in Article 37 paragraph (1) of Government Regulation Number 24 of 1997 concerning Land Registration which must include the deed of the Land Deed Making Official to register the right of land rights (behind the name) to the Land Office to create legal certainty and minimize the risks that occur in the future. However, in everyday life there is still a lot of buying and selling land that is not based on the laws and regulations that apply, namely only by using receipts and trust in each other. This is certainly very detrimental to both parties in the transfer of rights (behind the name), especially if the other party is not known to exist like the Case in Decision Number 42 / Pdt.G / 2010 / PN.Mtp

Visual asymmetries during face encoding Increased dwell time and fixations in the upper and left hemifields

2018 ◽  
Author(s):  
Fatima Maria Felisberti
Keyword(s):  
Face Recognition ◽  
Eye Movements ◽  
Visual Field ◽  
Face Processing ◽  
Dwell Time ◽  
The Other ◽  
Environmental Cues ◽  
Reading Habits ◽  
The Right

Visual field asymmetries (VFA) in the encoding of groups rather than individual faces has been rarely investigated. Here, eye movements (dwell time (DT) and fixations (Fix)) were recorded during the encoding of three groups of four faces tagged with cheating, cooperative, or neutral behaviours. Faces in each of the three groups were placed in the upper left (UL), upper right (UR), lower left (LL), or lower right (LR) quadrants. Face recognition was equally high in the three groups. In contrast, the proportion of DT and Fix were higher for faces in the left than the right hemifield and in the upper rather than the lower hemifield. The overall time spent looking at the UL was higher than in the other quadrants. The findings are relevant to the understanding of VFA in face processing, especially groups of faces, and might be linked to environmental cues and/or reading habits.

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