Related papers: A Note on Walk versus Wait: Lazy Mathematician Win…

The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…

This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…

This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…

Motivated by recent studies in human balance control, we study a delayed random walk with an unstable fixed point. It is observed that the random walker moves away from the unstable fixed point more slowly than is observed in the absence of…

The Halting Problem is a version of the Liar's Paradox.

In [arXiv:2409.00161v1 (2024)] Cavendish et al. raise three criticisms against our time of arrival proposal [L. Maccone and K. Sacha, Phys. Rev. Lett. 124, 110402 (2020)]. Here we show that all three criticisms are without merit. One of…

The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…

This is a correction to the afore-mentioned paper in Duke Math. J. vol. 75 (1994), 99-119 by S. Keel, K. Matsuki, and J. McKernan. We completely rewrite Chapter 6 according to the original manuscript of the second author, in order to fix…

I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only…

The condensation Probability Function defined in papers of X.R. Wang is criticized on many aspects. The modified latent heat and potential temperature are plotted and compared to usual atmospheric formulations.

The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968

We introduce and summarise results from the recent paper 'Biased random walk on the trace of biased random walk on the trace of ...', which was written jointly with M. P. Holmes (University of Melbourne). We also present additional…

In this paper we investigate the recent advances by Zhang, Maynard and Pintz towards Polignac's conjecture and give some new results concerning the relationship between Polignac numbers and arithmetic progressions.

This paper has been withdrawn by Wenji Deng (e-mail: [email protected]) for further modification at Oct. 12, 1998. {PACS: 03.75.Fi, 05.30.Jp.64.60.-i, 32.80.Pj}

A note on "Bayesian nonparametric estimators derived from conditional Gibbs structures" by Antonio Lijoi, Igor Pr\"{u}nster, Stephen G. Walker [arXiv:0808.2863].

We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case…

Comment on P. Walker, Nature 453 (2008) 864, http://www.nature.com/nature/journal/v453/n7197/full/453864a.html

In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on…

We show that the criticism of our paper [Phys. Rev. B 65, 125109 (2002)] by Wang, Millis, and Das Sarma [cond-mat/0206203] is based on a trivial mathematical mistake they have committed.

The authors discuss the role of controversy in mathematics as a preface to two opposing articles on computational complexity theory: "Some basic information on information-based complexity theory" by Beresford Parlett [math.NA/9201266] and…