Zobrazeno 1 - 10
of 4 064
pro vyhledávání: '"60C05"'
Autor:
Chatterjee, Sourav, Ray, Souvik
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do we get $n
Externí odkaz:
http://arxiv.org/abs/2410.21513
We investigate the best constant $J(n,d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on the hypercube $\{0,1\}^n$, where $s(f)$ denotes the sensitivity of $f$
Externí odkaz:
http://arxiv.org/abs/2410.19949
Autor:
Capannoli, F., Hollander, F. den
The present overview of interacting particle systems on random graphs collects the notes of a mini-course given by the authors at the Brazilian School of Probability, 5--9 August 2024, in Salvador, Bahia, Brazil. The content is a personal snapshot of
Externí odkaz:
http://arxiv.org/abs/2410.17766
We show that the set of atoms of the limiting empirical marginal distribution in the random $2$-SAT model is $\mathbb Q \cap (0,1)$, for all clause-to-variable densities up to the satisfiability threshold. While for densities up to $1/2$, the measure
Externí odkaz:
http://arxiv.org/abs/2410.17749
Autor:
Dubach, Victor
We study classical pattern counts in Mallows random permutations with parameters $(n,q_n)$, as $n\to\infty$. We focus on three different regimes for the parameter $q = q_n$. When $n^{3/2}(1-q)\to0$, we use coupling techniques to prove that pattern co
Externí odkaz:
http://arxiv.org/abs/2410.17228
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
Autor:
Ray, Souvik
In this paper, we shall try to deduce asymptotic behaviour of component spectrum of random $n \times n$ magical squares with line sum $r \in \mathbb{N}$, which can also be identified as $r$-regular bipartite graphs on $2n$ vertices, chosen uniformly
Externí odkaz:
http://arxiv.org/abs/2410.10334
Autor:
Meunier, Paul, Pournajafi, Pegah
We show that the bunkbed conjecture remains true when gluing along a vertex. As immediate corollaries, we obtain that the bunkbed conjecture is true for forests and that a minimal counterexample to the bunkbed conjecture is 2-connected.
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Externí odkaz:
http://arxiv.org/abs/2410.08957
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem shows tha
Externí odkaz:
http://arxiv.org/abs/2410.06807
Autor:
Bohman, Tom, Hofstad, Jakob
We show that the independence number of $ G_{n,m}$ is concentrated on two values for $ n^{5/4+ \epsilon} < m \le \binom{n}{2}$. This result establishes a distinction between $G_{n,m}$ and $G_{n,p}$ with $p = m/ \binom{n}{2}$ in the regime $ n^{5/4 +
Externí odkaz:
http://arxiv.org/abs/2410.05420