Zobrazeno 1 - 10
of 103
pro vyhledávání: '"05C80, 60K35"'
We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop $\mathrm{O}(1)$ model and then single random current exhibit a non-unique phase transition with respect to the inverse
Externí odkaz:
http://arxiv.org/abs/2410.22061
Autor:
Hollander, F. den
The present paper is a brief overview of random opinion dynamics on random graphs based on the Ising Lecture given by the author at the World Congress in Probability and Statistics, 12--16 August 2024, Bochum, Germany. The content is a snapshot of an
Externí odkaz:
http://arxiv.org/abs/2410.17808
Autor:
Diskin, Sahar, Geisler, Anna
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained from $G(i
Externí odkaz:
http://arxiv.org/abs/2409.14398
We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability l
Externí odkaz:
http://arxiv.org/abs/2407.18635
Autor:
Hollom, Lawrence
The bunkbed conjecture, which has featured in the folklore of probability theory since at least 1985, concerns bond percolation on the product graph $G\Box K_2$. We have two copies $G_0$ and $G_1$ of $G$, and if $x^{(0)}$ and $x^{(1)}$ are the copies
Externí odkaz:
http://arxiv.org/abs/2406.01790
Autor:
Diskin, Sahar, Geisler, Anna
For $t \in \mathbb{N}$ and every $i\in[t]$, let $H_i$ be a $d_i$-regular connected graph, with $1<|V(H_i)|\le C$ for some integer $C\ge 2$. Let $G=\square_{i=1}^tH_i$ be the Cartesian product of $H_1, \ldots, H_t$. We show that if $t\ge 5C\log_2C$ th
Externí odkaz:
http://arxiv.org/abs/2404.14020
We study cluster sizes in supercritical $d$-dimensional inhomogeneous percolation models with long-range edges -- such as long-range percolation -- and/or heavy-tailed degree distributions -- such as geometric inhomogeneous random graphs and the age-
Externí odkaz:
http://arxiv.org/abs/2404.02984
We study the volume of rigid loop-$O(n)$ quadrangulations with a boundary of length $2p$ in the non-generic critical regime. We prove that, as the half-perimeter $p$ goes to infinity, the volume scales in distribution to an explicit random variable.
Externí odkaz:
http://arxiv.org/abs/2402.04827
Autor:
Krivelevich, Michael
We present a relatively short and self-contained proof of the classical result on component sizes in the supercritical percolation on the high dimensional binary cube, due to Ajtai, Koml\'os and Szemer\'edi (1982) and to Bollob\'as, Kohayakawa and \L
Externí odkaz:
http://arxiv.org/abs/2311.07210
We provide a sufficient condition on the isoperimetric properties of a regular graph $G$ of growing degree $d$, under which the random subgraph $G_p$ typically undergoes a phase transition around $p=\frac{1}{d}$ which resembles the emergence of a gia
Externí odkaz:
http://arxiv.org/abs/2308.10267