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pro vyhledávání: '"Aldous, David"'
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, Pittel, Boris
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to $1/{i(m-i)}$. We stu
Externí odkaz:
http://arxiv.org/abs/2302.05066
Let $(A_u : u \in \mathbb{B})$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $ \mathbb{B}$. Each car tries to park on its arrival node, but if it is already occupied, it drives towards the r
Externí odkaz:
http://arxiv.org/abs/2205.15932
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