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pro vyhledávání: '"D'Addario A"'
Autor:
Addario-Berry, Louigi, Fontaine, Catherine, Khanfir, Robin, Langevin, Louis-Roy, Têtu, Simone
We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with probability at
Externí odkaz:
http://arxiv.org/abs/2411.18614
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric structure
Externí odkaz:
http://arxiv.org/abs/2410.13152
In this note we analyze the performance of a simple root-finding algorithm in uniform attachment trees. The leaf-stripping algorithm recursively removes all leaves of the tree for a carefully chosen number of rounds. We show that, with probability $1
Externí odkaz:
http://arxiv.org/abs/2410.06481
The Horton-Strahler number of a rooted tree $T$ is the height of the tallest complete binary tree that can be homeomorphically embedded in $T$. The number of full binary trees with $n$ internal vertices and Horton-Strahler number $s$ is known to be t
Externí odkaz:
http://arxiv.org/abs/2406.03025
Autor:
Berry, Louigi Addario, Briend, Simon, Devroye, Luc, Donderwinkel, Serte, Kerriou, Céline, Lugosi, Gábor
We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and connecting
Externí odkaz:
http://arxiv.org/abs/2403.20185
Let ${\mathbf T}_n$ be a uniformly random tree with vertex set $[n]=\{1,\ldots,n\}$, let $\Delta_{{\mathbf T}_n}$ be the largest vertex degree in ${\mathbf T}_n$, and let $\lambda_1({\mathbf T}_n),\ldots,\lambda_n({\mathbf T}_n)$ be the eigenvalues o
Externí odkaz:
http://arxiv.org/abs/2403.08443
The height of a random PATRICIA tree built from independent, identically distributed infinite binary strings with arbitrary diffuse probability distribution $\mu$ on $\{0,1\}^\mathbb{N}$ is studied. We show that the expected height grows asymptotical
Externí odkaz:
http://arxiv.org/abs/2403.05269
Autor:
D'Addario, Anthony, Kuan, Johnathan, Opondo, Noah F., Erturk, Ozan, Zhou, Tao, Bhave, Sunil A., Holt, Martin V., Fuchs, Gregory D.
Bulk-mode acoustic waves in a crystalline material exert lattice strain through the thickness of the sample, which couples to the spin Hamiltonian of defect-based qubits such as the nitrogen-vacancy (NV) center defect in diamond. This mechanism has b
Externí odkaz:
http://arxiv.org/abs/2312.06862
Publikováno v:
Phys. Rev. D 109, 084046 (2024)
Deviations from General Relativity can alter the quasi-normal mode (QNM) ringdown of perturbed black holes. It is known that a shift-symmetric (hence massless) scalar can only introduce black hole hair if it couples to the Gauss-Bonnet invariant, in
Externí odkaz:
http://arxiv.org/abs/2311.17666
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaym\'e trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions with
Externí odkaz:
http://arxiv.org/abs/2311.06163