A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (01) ◽  
pp. 169-175
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b > 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 <m <a) under different conditions.

A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b > 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 <m <a) under different conditions.

Hanna Yablonka, Yeladim beseder gamur: biyografiyah dorit shel yelidei haaretz 1948–1955 (Children by the Book, Biography of a Generation: The First Native Israelis Born 1948–1955). Rishon Letziyon: Miskal, 2018. 430 pp.

2021 ◽  
pp. 310-312
Keyword(s):  
Educational System ◽  
Historical Consciousness ◽  
The State ◽  
Historical Experience ◽  
One Dimensional ◽  
The People ◽  
Native Identity ◽  
The One ◽  
State Educational ◽  
The Right

This chapter examines Hanna Yablonka's Children by the Book, Biography of a Generation: The First Native Israelis Born 1948–1955 (2018). This book is unique in that it is neither politically committed to nationalist political slogans that are thrown daily into the arena of Israeli politics in the days of Netanyahu nor connected to the one-dimensional, sweeping condemnation of critics of the Israeli enterprise on the Right and Left. Instead, it suggests to set aside, even if only for a moment, what Yablonka calls “the current Israeli discourse, which furiously shatters everything that has happened in the state since it was established, brutally erasing all the achievements of Little Israel.” Yabonka is guided by Karl Mannheim's concept of a “historical generation”: a group in which there is a shared historical consciousness derived from historical experience. She shows how the state educational system fashioned the image of the new Israeli, endowing children with a local, native identity and imbuing them with the consciousness of belonging both to the people and to the land.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

scholarly journals Zero-one-only process: A correlated random walk with a stochastic ratchet

2014 ◽  
Vol 28 (29) ◽  
pp. 1450201
Author(s):  
Seung Ki Baek ◽  
Hawoong Jeong ◽  
Seung-Woo Son ◽  
Beom Jun Kim
Keyword(s):  
Transport Phenomenon ◽  
Random Walk ◽  
Random Walks ◽  
Stochastic Processes ◽  
Function Method ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Persistent Random Walk ◽  
The One ◽  
Previous Step

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability p, and stops to change the direction with 1 − p. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

The random walk associated by the game of roulette

1981 ◽  
Vol 18 (04) ◽  
pp. 931-936
Author(s):  
James M. Hill ◽  
Chandra M. Gulati
Keyword(s):  
Random Walk ◽  
Power Series ◽  
Generating Functions ◽  
The Right ◽  
Lagrange's Theorem ◽  
Explicit Expressions

The random walk arising in the game of roulette involves an absorbing barrier at the origin; at each step either a unit displacement to the left or a fixed multiple displacement to the right can occur with probabilities q and p respectively. Using generating functions and Lagrange's theorem for the expansion of a function as a power series explicit expressions are deduced for the probabilities of the player's capital at the nth step.

scholarly journals Odd and Even Major Indices and One-Dimensional Characters for Classical Weyl Groups

2020 ◽  
Vol 24 (4) ◽  
pp. 809-835
Author(s):  
Francesco Brenti ◽  
Paolo Sentinelli
Keyword(s):  
Generating Functions ◽  
Weyl Groups ◽  
One Dimensional ◽  
Major Index ◽  
The One

Abstract We define and study odd and even analogues of the major index statistics for the classical Weyl groups. More precisely, we show that the generating functions of these statistics, twisted by the one-dimensional characters of the corresponding groups, always factor in an explicit way. In particular, we obtain odd and even analogues of Carlitz’s identity, of the Gessel–Simion Theorem, and a parabolic extension, and refinement, of a result of Wachs.

On Certain Probability Models in Random Walk

1972 ◽  
Vol 21 (1-2) ◽  
pp. 71-76 ◽  
Author(s):  
Kanwar Sen ◽  
Y. L. Ahuja
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
Two Dimensional ◽  
Probability Models ◽  
Unit Step

This paper considers a two dimensional random walk in which a particle moves from its position a unit step either horizontally, or vertically, or diagonally forward or stay there with respective probabilities p, q, r and s ( p + q + r + s= 1). The probabilities that initially at (0, 0}, the position of the particle is ( x, y) at time t+ 0 after having in the line y = x, ( i) h crosses and (ii) g hits and b slips, have been determined alongwith their generating functions.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

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