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of 2 794
pro vyhledávání: '"A, Ottolini"'
Autor:
Ottolini, Andrea, Chen, Ray
We analyze the mixing time of a popular shuffling machine known as the shelf shuffler. It is a modified version of a $2m$-handed riffle shuffle ($m=10$ in casinos) in which a deck of $n$ cards is split multinomially into $2m$ piles, the even-numbered
Externí odkaz:
http://arxiv.org/abs/2410.17345
Autor:
Ottolini, Andrea
Given a large connected graph $G=(V,E)$, and two vertices $w,\neq v$, let $T_{w,v}$ be the first hitting time to $v$ starting from $w$ for the simple random walk on $G$. We prove a general theorem that guarantees, under some assumptions on $G$, to ap
Externí odkaz:
http://arxiv.org/abs/2402.09624
Autor:
Dudarov, William, Feinberg, Noah, Guo, Raymond, Goh, Ansel, Ottolini, Andrea, Stepin, Alicia, Tripathi, Raghavenda, Zhang, Joia
Let $G=(V,E)$ be a finite, simple, connected, combinatorial graph on $n$ vertices and let $D \in \mathbb{R}^{n \times n}$ be its graph distance matrix $D_{ij} = d(v_i, v_j)$. Steinerberger (J. Graph Theory, 2023) empirically observed that the linear
Externí odkaz:
http://arxiv.org/abs/2307.04740
We consider the optimal transport problem between a set of $n$ red points and a set of $n$ blue points subject to a concave cost function such as $c(x,y) = \|x-y\|^{p}$ for $0< p < 1$. Our focus is on a particularly simple matching algorithm: match t
Externí odkaz:
http://arxiv.org/abs/2307.03140
We consider Erd\H{o}s-R\'enyi graphs $G(n,p)$ for $0 < p < 1$ fixed and $n \rightarrow \infty$ and study the expected number of steps, $H_{wv}$, that a random walk started in $w$ needs to first arrive in $v$. A natural guess is that an Erd\H{o}s-R\'e
Externí odkaz:
http://arxiv.org/abs/2304.04289
Publikováno v:
J. Appl. Probab. 61 (2024) 654-666
Consider a well-shuffled deck of cards of $n$ different types where each type occurs $m$ times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is remove
Externí odkaz:
http://arxiv.org/abs/2303.15601
Let $G=(V,E)$ be a finite, combinatorial graph. We define a notion of curvature on the vertices $V$ via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. Graphs with curvature
Externí odkaz:
http://arxiv.org/abs/2302.06021
The problem of connecting the operator parameters that label the same self-adjoint extension of a given symmetric operator, respectively, within the 'absolute' von Neumann extension scheme and the 'relative' boundary-triplet-induced extension scheme
Externí odkaz:
http://arxiv.org/abs/2212.07137
We consider the following game that has been used as a way of testing claims of extrasensory perception (ESP). One is given a deck of $mn$ cards comprised of $n$ distinct types each of which appears exactly $m$ times: this deck is shuffled and then c
Externí odkaz:
http://arxiv.org/abs/2211.09094
Autor:
Gerencsér, Balázs, Ottolini, Andrea
We analyze the convergence rates for a family of auto-regressive Markov chains $(X^{(n)}_k)_{k\geq 0}$ on $\mathbb R^d$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The interest in the
Externí odkaz:
http://arxiv.org/abs/2209.01474