Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of blanket times for sequences of random walks on critical
  random graphs   Under the assumption that sequences of graphs equipped with resistances,
associated measures, walks and local times converge in a suitable
Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution
of the $\varepsilon$-blanket times of the random walks in the sequence. The
precise nature of these bounds ensures convergence of the $\varepsilon$-blanket
times of the random walks if the $\varepsilon$-blanket time of the limiting
diffusion is continuous with probability one at $\varepsilon$. This result
enables us to prove annealed convergence in various examples of critical random
graphs, including critical Galton-Watson trees, the Erd\H{o}s-R\'enyi random
graph in the critical window and the configuration model in the scaling
critical window. We highlight that proving continuity of the
$\varepsilon$-blanket time of the limiting diffusion relies on the scale
invariance of a finite measure that gives rise to realizations of the limiting
compact random metric space, and therefore we expect our results to hold for
other examples of random graphs with a similar scale invariance property.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci