Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A revisited proof of the Seneta-Heyde norming for branching random walks
  under optimal assumptions   We introduce a set of tools which simplify and streamline the proofs of limit
theorems concerning near-critical particles in branching random walks under
optimal assumptions. We exemplify our method by giving another proof of the
Seneta-Heyde norming for the critical additive martingale, initially due to
A\"id\'ekon and Shi. The method involves in particular the replacement of
certain second moment estimates by truncated first moment bounds, and the
replacement of ballot-type theorems for random walks by estimates coming from
an explicit expression for the potential kernel of random walks killed below
the origin. Of independent interest might be a short, self-contained proof of
this expression, as well as a criterion for convergence in probability of
non-negative random variables in terms of conditional Laplace transforms.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int