Related papers: The Distribution Route from Ancestors to Descendan…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the…

This note gives a proof of an improved upper bound for the right-side tail of a distribution discussed in "Crossover Distributions at the Edge of the Rarefaction Fan" by Ivan Corwin and Jeremy Quastel.

In this paper, we proposed an evolving model via the hypergraph to illustrate the evolution of the citation network. In the evolving model, we consider the mechanism combined with preferential attachment and the aging influence. Simulation…

We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxiv.org:math/0809.1635.

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…

We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections we derive various combinatorial…

This is a comment on the paper arXiv:1410.2840 by Ji and Jin, to appear in the AOAS.

Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].

We study the genus expansion of Barannikov-Kontsevich solutions of the WDVV equation. In terms of the related graph calculus we give a definition of descendants at one point and prove that this definition satisfies the topological recursion…

The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.

The recently discovered correspondence between the distribution of rapidity gaps in electron-nucleus diffractive processes and the statistics of the height of genealogical trees in branching random walks is reviewed. In addition, a new…

The content of this paper is now available as part of arXiv:0802.2019

This is a translation of the diploma thesis of Thomas Br\"ustle, Darstellungsk\"ocher der erblichen Algebren vom Typ $\tilde{A}_n$, written in German, at the University of Zurich, August 1990. Supervisor: P. Gabriel. Translated by K. Baur,…

A growing literature provides evidence on multigenerational inequality -- the extent to which socio-economic advantages persist across three or more generations. This chapter reviews its main findings and implications. Most studies find…

In this note, we prove a conjecture proposed by Tao Zhang, Shuxing Li, Tao Feng and Gennian Ge, IEEE Transaction on Information Theory, vol. 60, no. 5, May 2014. This conjecture is about the cross correlation distribution of ternary…

Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it…

We review the results of our previous publication [Phys. Rev. D63, 116001 (2001); hep-ph/0012226] in the light of recent calculations and comments.

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…