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The Random Walk Path of Pál Révész in Probability

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (15 November 2024) | Viewed by 1681

Special Issue Editors


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Guest Editor
Department of Mathematics, College of Staten Island, City University of New York, New York, NY 10314, USA
Interests: Brownian motion; random walk; local time; additive functionals; anisotropic random walk

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Guest Editor
Alfréd Rényi Institute of Mathematics, 1364 Budapest, Hungary
Interests: Brownian motion; random walk; local time; additive functionals; anisotropic random walk

Special Issue Information

Dear Colleagues,

Pál Révész, the world-renowned Hungarian probability theorist, passed away in 2022—he had been an extremely prolific mathematician, with 200 research papers and four books under his belt. A graduate of Eötvös Lóránd University, Révész spent decades as the head of the Probability Department of the Rényi Institute, before heading the Department of Statistics and Probability of the Vienna University of Technology. Additionally, he had been a visiting professor at numerous schools across Europe and Canada.

In 1982, he was selected to become a member of the Hungarian Academy and served as the president of the Bernoulli Society of Mathematical Statistics and Probability from 1983 to 1985, ultimately becoming a member of the Academy Europaea in 1991.

His groundbreaking work in many areas of probability theory are best reflected in the titles of his influential books: Laws of large numbers (1968), Strong approximation in Probability and Statistics (1981, together with Miklós Csörgő), Random Walks of Infinitely Many Particles (1990), and Random walk in Random and Non-Random Environments (1994, 2005, 2013). Please refer to the article In memoriam Pál Révész (1934–2022).

As a person, he was beyond generous in his collaborations, always happy to talk about the problems he was working on. He listened with the same respect and curiosity whether talking to a famous professor or an eager student, and he loved being able to help a new generation of mathematicians.

Beyond mathematics, he loved classical music, long walks, and the company of friends, but he admitted that during the concerts and the long walks he was still working on mathematics in his head.

In this volume we seek to gather together the papers of his coworkers, friends, and colleagues to commemorate his life and his everlasting impact on probability theory. Submissions from people working on random walk topics, who feel that their research was influenced by the work of Pál Révész, are also welcome.

Prof. Dr. Antónia Földes
Prof. Dr. Endre Csáki
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • laws of large numbers
  • random walk
  • Wiener process
  • strong approximation of the random walks and its local time
  • anisotropic walk

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Published Papers (2 papers)

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Research

8 pages, 228 KiB  
Article
Two Monotonicity Results for Beta Distribution Functions
by Kurt Hornik
Entropy 2024, 26(11), 938; https://doi.org/10.3390/e26110938 - 31 Oct 2024
Viewed by 436
Abstract
Write pbeta(·,α,β) for the distribution function of the Beta distribution with parameters α and β. We show that αpbeta(α/(α+β),α,β) is [...] Read more.
Write pbeta(·,α,β) for the distribution function of the Beta distribution with parameters α and β. We show that αpbeta(α/(α+β),α,β) is decreasing and αpbeta(α/(α+β),α+1,β) is increasing over the positive reals, with the common limit for α expressible in terms of the Gamma distribution functions, and discuss implications for the distribution functions of the Gamma, Poisson and Binomial distributions. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
8 pages, 262 KiB  
Article
Random Walks and Lorentz Processes
by Domokos Szász
Entropy 2024, 26(11), 908; https://doi.org/10.3390/e26110908 - 25 Oct 2024
Viewed by 489
Abstract
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical systems. Here we first present an example [...] Read more.
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical systems. Here we first present an example where the method based on the probabilistic approach led to new results for the Lorentz process: concretely, the recurrence of the planar periodic Lorentz process with a finite horizon. Afterwards, an unsolved problem—related to a 1981 question of Sinai on locally perturbed periodic Lorentz processes—is formulated as an analogous problem in the language of random walks. Full article
(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)
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