Zobrazeno 1 - 10
of 934
pro vyhledávání: '"JANSON, SVANTE"'
Autor:
Janson, Svante, Lo, Tiffany Y. Y.
We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment graph. In this model, vertices are sequentially added, each born with outdegree
Externí odkaz:
http://arxiv.org/abs/2412.13975
Autor:
Aldous, David, Janson, Svante
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$. The heigh
Externí odkaz:
http://arxiv.org/abs/2412.12319
Autor:
Aldous, David J., Janson, Svante
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$. Study of
Externí odkaz:
http://arxiv.org/abs/2412.09655
The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost
Externí odkaz:
http://arxiv.org/abs/2408.06817
The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained "probability" treatmen
Externí odkaz:
http://arxiv.org/abs/2405.05102
Autor:
Janson, Svante
Most of the results in the paper for Patricia tries have earlier been proved by Jaspar Ischebeck. We study the distribution of fringe trees in Patricia tries and compressed binary search trees; both cases are random binary trees that have been compre
Externí odkaz:
http://arxiv.org/abs/2405.01239
Autor:
Janson, Svante, Smith, Warren D.
Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but distinct from,
Externí odkaz:
http://arxiv.org/abs/2403.02670
Autor:
Janson, Svante
Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the game is played for $3n$ rounds, but one of the two players is restricted
Externí odkaz:
http://arxiv.org/abs/2402.14676
Autor:
Janson, Svante
We consider triangular P\'olya urns and show under very weak conditions a general strong limit theorem of the form $X_{ni}/a_{ni}\to \mathcal{X}_i$ a.s., where $X_{ni}$ is the number of balls of colour $i$ after $n$ draws; the constants $a_{ni}$ are
Externí odkaz:
http://arxiv.org/abs/2402.01299
Autor:
Janson, Svante
Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization to a Gaus
Externí odkaz:
http://arxiv.org/abs/2312.13823