Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Deviations in $\beta$-ensembles and Law of Iterated Logarithm in
  Last Passage Percolation   For the last passage percolation (LPP) on $\mathbb{Z}^2$ with exponential
passage times, let $T_{n}$ denote the passage time from $(1,1)$ to $(n,n)$. We
investigate the law of iterated logarithm of the sequence $\{T_{n}\}_{n\geq
1}$; we show that $\liminf_{n\to \infty} \frac{T_{n}-4n}{n^{1/3}(\log \log
n)^{1/3}}$ almost surely converges to a deterministic negative constant and
obtain some estimates on the same. This settles a conjecture of Ledoux (J.
Theor. Probab., 2018) where a related lower bound and similar results for the
corresponding upper tail were proved. Our proof relies on a slight shift in
perspective from point-to-point passage times to considering point-to-line
passage times instead, and exploiting the correspondence of the latter to the
largest eigenvalue of the Laguerre Orthogonal Ensemble (LOE). A key technical
ingredient, which is of independent interest, is a new lower bound of lower
tail deviation probability of the largest eigenvalue of $\beta$-Laguerre
ensembles, which extends the results proved in the context of the
$\beta$-Hermite ensembles by Ledoux and Rider (Electron. J. Probab., 2010).

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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th