Dr. Mohamed Abdelkader

Statistics and operations research, King Saud University, Riyadh, Ar Riyāḑ, Saudi Arabia

Dr. Mohamed Abdelkader

Statistics and operations research, King Saud University, Riyadh, Ar Riyāḑ, Saudi Arabia

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Academic Career Length

4Years (2023-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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9 May 2023 in Symmetry

Journal Article

Two-Dimensional Moran Model

Asma Althagafi

Mohamed Abdelkader

In this paper, we consider a two-dimensional Moran model of random walks consisting of two queues evolving in parallel which can (at each unit of time) either increase by one or reset to 0. We analyze the joint law of their final altitude and prove that the asymptotic distribution of each component is a shifted geometric distribution and we analyze the maximum of these two components, also giving closed forms for the mean and variance.

2 September 2023 in Mathematics

Journal Article

Two-Dimensional Moran Model: Final Altitude and Number of Resets

Rafik Aguech

Mohamed Abdelkader

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude

Z_{n}

. Finally, we analyse the statistical properties of

N_{n}^{X}

, the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function.

1 November 2023 in Mathematics

Journal Article

On the Height of One-Dimensional Random Walk

Mohamed Abdelkader

Consider the one-dimensional random walk

X_{n}

: as it evolves (at each unit of time), it either increases by one with probability p or resets to 0 with probability

1 - p

. In the present paper, we analyze the law of the height statistics

H_{n}

, corresponding to our model

X_{n}

. Also, we prove that the limiting distribution of the walk

X_{n}

is a shifted geometric distribution with parameter

1 - p

and find the closed forms of the mean and the variance of

X_{n}

using the probability-generating function.

4 June 2025 in Complex Analysis and Operator Theory

Journal Article

Study of the degenerate Lévy-Meixner Appell polynomials via falling operators

23 November 2023 in Axioms

Journal Article

Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1]

Mohamed Abdelkader

In this paper, we provide the decay of correlations for random dynamical systems. Precisely, we consider the uniformly

C^{2}

piecewise expanding maps defined on the unit interval satisfying

λ (T_{ω}^{'}) = inf | T_{ω}^{'} | > 2

. As a principal tool of these studies, we use a coupling method for analyzing the coupling time of observables with bounded variation.

1 January 2024 in AIMS Mathematics

Journal Article

Moran random walk with reset and short memory

Mohamed Abdelkader

Rafik Aguech

We investigated the statistical properties of the Moran random walk $ (Y_n)_n $ in one dimension, focusing on short memory. Specifically, employing generating function techniques, we determined the cumulative distribution function and the mean of the height $ H_n $. Furthermore, we derived explicit expressions for the distribution, mean, and variance of $ Y_n $, along with its asymptotic distribution. Finally, we provided the distribution of the waiting time $ \tau_h $, which represents the number of steps required to reach a specified level $ h $, as the conclusion of our study.

About Me

I am Mohamed Abdelkader from Tunisia, a Doctor in mathematics and applications. I obtained my Bachelor's degree in Mathematics in 2009 at Carthage University and my Master's degree at El-Manar University in 2013, and I finished my studies and obtained a Ph.D. at Toulon University and Safx University in November 2017. I work on the statistical properties of random dynamical systems, such as the central limit theorem, and how the invariance principle decays the correlations of uniformly expanding maps. Now, my work is concentrating on the statistical properties of the Moran model with respect to the distribution of the final altitude. I have been an Assistant Professor at King Saud University for the past five years (from September 2018 to present). I teach many courses, such as regression analysis, statistical packages, and analysis. I taught for two years in Tunisia at the University of Sousse and the University of Kairouan. In my previous research, I wanted to find a relationship between dynamical systems and the statistical properties of the random walk. I wanted to examine the distribution of the orbit length such that the random dynamical system satisfies the first return time on the probability space. I am a member of the Statistics Committee of the Department of Statistics and Operations in the Faculty of Science at King Saud University.

Dr. Mohamed Abdelkader

Dr. Mohamed Abdelkader

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