Zobrazeno 1 - 10
of 370
pro vyhledávání: '"Aldous, A. J."'
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 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:
Aldous, David J., Feng, Shi
Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $\theta \in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($\theta$) samples, and jump to the $j$'th
Externí odkaz:
http://arxiv.org/abs/2404.01348
Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $\theta \in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($\theta$) samples, and jump to the $j$'th
Externí odkaz:
http://arxiv.org/abs/2403.18153
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose support contain
Externí odkaz:
http://arxiv.org/abs/2403.10926
Autor:
Aldous, David J., Bruss, F. Thomas
Publikováno v:
A final version is published as {\em Amer. Math. Monthly} 130 (2023) 303--320
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived advantage based
Externí odkaz:
http://arxiv.org/abs/2312.10331
Autor:
Aldous, David J., Janson, Svante
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively (from the root) 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
Externí odkaz:
http://arxiv.org/abs/2303.02529
Autor:
Aldous, David J., Cruz, Madelyn
Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for mixing human pl
Externí odkaz:
http://arxiv.org/abs/2106.09142
Autor:
Aldous, David J.
Is there a constant $r_0$ such that, in any invariant tree network linking rate-$1$ Poisson points in the plane, the mean within-network distance between points at Euclidean distance $r$ is infinite for $r > r_0$? We prove a slightly weaker result. T
Externí odkaz:
http://arxiv.org/abs/2103.00669
Autor:
Aldous, David J.
Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric models, and with the discrete coupon collector's problem and with cover times for finite Markov chain
Externí odkaz:
http://arxiv.org/abs/2101.12671