Rahul Roy
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Rahul Roy has a total of 36 co-authors. Here are the top co-authors by number of shared publications:
- Hideki Tanemura
Keio University
10 shared publications - Masato Takei
Yokohama National University
6 shared publications - Afshin Parvardeh
Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran
2 shared publications - Arpan Mukhopadhyay
University of Warwick, Coventry, United Kingdom
2 shared publications - Azadeh Parvaneh
Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran
2 shared publications - Farkhondeh Alsadat Sajadi
University of Isfahan
2 shared publications
Latest Publications
- 19 October 2026
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- p. 1
Scaling limit of a drainage network model on a perturbed lattice – CORRIGENDUM
- 19 October 2026
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- p. 1
Scaling limit of a drainage network model on a perturbed lattice – CORRIGENDUM
- 9 September 2026
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- p. 1-47
Scaling limit of a drainage network model on a perturbed lattice
The study of random networks generally requires that vertices be independently and uniformly distributed over disjoint regions such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a drainage network model constructed on a random subset of double struck upper Z squared $\mathbb{Z}^2$ , where points in double struck upper Z squared $\mathbb{Z}^2$ are randomly perturbed such that both horizontal and vertical perturbations are given by exponentially decaying discrete random variables with unbounded support and edges between two such points are specified according to the distance between them. We restrict vertical perturbations in the upward direction only. Here we establish that (i) the resultant stochastic network is a single tree almost surely and (ii) as a collection of paths, under diffusive scaling the resulting network converges to the Brownian web.- 9 September 2026
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- p. 1-47
Scaling limit of a drainage network model on a perturbed lattice
The study of random networks generally requires that vertices be independently and uniformly distributed over disjoint regions such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a drainage network model constructed on a random subset of double struck upper Z squared $\mathbb{Z}^2$ , where points in double struck upper Z squared $\mathbb{Z}^2$ are randomly perturbed such that both horizontal and vertical perturbations are given by exponentially decaying discrete random variables with unbounded support and edges between two such points are specified according to the distance between them. We restrict vertical perturbations in the upward direction only. Here we establish that (i) the resultant stochastic network is a single tree almost surely and (ii) as a collection of paths, under diffusive scaling the resulting network converges to the Brownian web.- 24 November 2025
- Published by Springer Nature in Indian Journal of Pure and Applied Mathematics
- Vol. 57 (1) , 215-233
Elephant random walk with varying memory
- 24 November 2025
- Published by Springer Nature in Indian Journal of Pure and Applied Mathematics
- Vol. 57 (1) , 215-233
Elephant random walk with varying memory
- 16 January 2025
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 62 (3) , 997-1009
The elephant random walk in the triangular array setting
Gut and Stadmüller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of the results by Gut and Stadtmüller (2022) for an ‘increasing memory’ version of the elephant random walk without stops. Here we present a formal definition of the process that was hinted at by Gut and Stadtmüller. This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtmüller (2022) for the elephant random walk, possibly with stops. We also obtain the central limit theorem for the supercritical case of this model.
- 16 January 2025
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 62 (3) , 997-1009
The elephant random walk in the triangular array setting
Gut and Stadmüller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of the results by Gut and Stadtmüller (2022) for an ‘increasing memory’ version of the elephant random walk without stops. Here we present a formal definition of the process that was hinted at by Gut and Stadtmüller. This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtmüller (2022) for the elephant random walk, possibly with stops. We also obtain the central limit theorem for the supercritical case of this model.
- 6 December 2024
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 90 (1) , 1-27
On a model of evolution of subspecies
Ben-Ari and Schinazi (J Stat Phys 162:415–425, 2016) introduced a stochastic model to study ‘virus-like evolving population with high mutation rate’. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0, 1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fitness. We change this to incorporate the notion of ‘survival of the fittest’, by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness f with a probability proportional to the size of the population of fitness f. Also death just removes one individual with the least fitness. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (J Stat Phys 162:415–425, 2016).
- 6 December 2024
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 90 (1) , 1-27
On a model of evolution of subspecies
Ben-Ari and Schinazi (J Stat Phys 162:415–425, 2016) introduced a stochastic model to study ‘virus-like evolving population with high mutation rate’. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0, 1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fitness. We change this to incorporate the notion of ‘survival of the fittest’, by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness f with a probability proportional to the size of the population of fitness f. Also death just removes one individual with the least fitness. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (J Stat Phys 162:415–425, 2016).
- Open AccessHow often can two independent elephant random walks on $\mathbb{Z}$ meet?We show that two independent elephant random walks on the integer lattice $\mathbb{Z}$ meet each other finitely often or infinitely often depends on whether the memory parameter $p$ is strictly larger than $3/4$ or not. Asymptotic results for the distance between them are also obtained.Open AccessHow often can two independent elephant random walks on $\mathbb{Z}$ meet?We show that two independent elephant random walks on the integer lattice $\mathbb{Z}$ meet each other finitely often or infinitely often depends on whether the memory parameter $p$ is strictly larger than $3/4$ or not. Asymptotic results for the distance between them are also obtained.
- Open Access
The elephant random walk in the triangular array setting
Gut and Stadmüller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtmüller (2022) for an "increasing memory" version of the elephant random walk without stops. Here we present a formal definition of the process which has been hinted at Eq. (2.2) in Gut and Stadtmüller (2022). This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtmüller (2022) for the elephant random walk, possibly with stops. We also obtain the CLT for the supercritical case of this model.
Open AccessThe elephant random walk in the triangular array setting
Gut and Stadmüller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtmüller (2022) for an "increasing memory" version of the elephant random walk without stops. Here we present a formal definition of the process which has been hinted at Eq. (2.2) in Gut and Stadtmüller (2022). This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtmüller (2022) for the elephant random walk, possibly with stops. We also obtain the CLT for the supercritical case of this model.
- Open Access
Phase transitions for a unidirectional elephant random walk with a power law memory
For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter $p$ and the power law exponent $β$, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, and the other two phases are distinguished by the speed at which the elephant travels.Open AccessPhase transitions for a unidirectional elephant random walk with a power law memory
For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter $p$ and the power law exponent $β$, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, and the other two phases are distinguished by the speed at which the elephant travels. - Open Access
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Communications in Probability
- Vol. 29 (none) , 1-12
Phase transitions for a unidirectional elephant random walk with a power law memory
For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter p and the power law exponent β, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, in the other phase there is a positive probability that the elephant travels an infinite distance and in the third phase the elephant travels an infinite distance with probability 1. For the critical case of the transition from the first phase to the second phase, the proof of our result requires coupling with a multi-type branching process.
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Communications in Probability
- Vol. 29 (none) , 1-12
Open AccessPhase transitions for a unidirectional elephant random walk with a power law memory
For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter p and the power law exponent β, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, in the other phase there is a positive probability that the elephant travels an infinite distance and in the third phase the elephant travels an infinite distance with probability 1. For the critical case of the transition from the first phase to the second phase, the proof of our result requires coupling with a multi-type branching process.
- 19 December 2023
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 190 (12) , 1-44
Two Directed Non-planar Random Networks and Their Scaling Limits
- 19 December 2023
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 190 (12) , 1-44
Two Directed Non-planar Random Networks and Their Scaling Limits