Related papers: A Note on Walk versus Wait: Lazy Mathematician Win…
In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…
In the recent review article, P.Markos admits that practically all numerical results on the critical behavior near the Anderson transition are in conflict with analytical expectations, but no serious discussion of this fact is given. The…
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.
Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From the $L^2$ analyticity of the Markov operator $P$, we deduce that an iterate of odd exponent of $P$ is `lazy', that is there exists an integer $k$ such that the…
This dissertation collects together results on Patience Sorting and its generalizations. It incorporates the results of math.CO/0506358, math.CO/0507031, and math.CO/0512122, as well as previously unpublished results.
The matrix analogues of Laplace's method and Watson's lemma are derived via the approach described by Williams and Wong [J. Approx. Theory 24 (4) (1974), 378-384]. Some examples are also given.
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.
We comment on the recent paper by Yuan Qing-Xin and Du Yin-Xiao (Eur. J. Phys. 29 (2008) N43-N45).
Comment on paper by Blanchette and Zhang, Phys. Rev. Lett. 102, 144501 (2009).
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
In the simple random walk the steps are independent, whereas in the Elephant Random Walk (ERW), which was introduced by Sch\"utz and Trimper in 2004, the next step always depends on the whole path so far. In an earlier paper we investigated…
Kane and Mertz's 2012 AMS Notices article "Debunking Myths about Gender and Mathematics Performance" claims to have debunked the greater male variability hypothesis with respect to mathematics abilities. The logical and statistical…
We consider planar lattice walks that start from (0,0), remain inthe first quadrant i, j >= 0, and are made of three types of steps: North-East, West and South. These walks are known to have remarkable enumerative and probabilistic…
The paper of Unal [J. Math. Phys. 59, 062104 (2018)], though worthy of attention, contains a conclusion that is in error and may mislead the efforts to extend his results. The aim of the present note is twofold: we provide a correction to…
This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…
This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains,…
We comment on the paper by M. W. Mitchell and R. Y. Chiao, ``Causality and negative group delay in a simple bandpass amplifier", Am. J. Phys. 66 (1), 14-19 (1998).
The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner [8].
Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight?…
The Lonely Runner Conjecture was posed independently by Wills and Cusick and has many applications in different mathematical fields, such as diophantine approximation. This well-known conjecture states that for any set of runners running…