Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quenched Invariance Principle for a class of random conductance models
  with long-range jumps   We study random walks on $\mathbb Z^d$ (with $d\ge 2$) among stationary
ergodic random conductances $\{C_{x,y}\colon x,y\in\mathbb Z^d\}$ that permit
jumps of arbitrary length. Our focus is on the Quenched Invariance Principle
(QIP) which we establish by a combination of corrector methods, functional
inequalities and heat-kernel technology assuming that the $p$-th moment of
$\sum_{x\in\mathbb Z^d}C_{0,x}|x|^2$ and $q$-th moment of $1/C_{0,x}$ for $x$
neighboring the origin are finite for some $p,q\ge1$ with $p^{-1}+q^{-1}<2/d$.
In particular, a QIP thus holds for random walks on long-range percolation
graphs with connectivity exponents larger than $2d$ in all $d\ge2$, provided
all the nearest-neighbor edges are present. Although still limited by moment
conditions, our method of proof is novel in that it avoids proving
everywhere-sublinearity of the corrector. This is relevant because we show
that, for long-range percolation with exponents between $d+2$ and $2d$, the
corrector exists but fails to be sublinear everywhere. Similar examples are
constructed also for nearest-neighbor, ergodic conductances in $d\ge3$ under
the conditions complementary to those of the recent work of P. Bella and M.
Sch\"affner. These examples elucidate the limitations of elliptic-regularity
techniques that underlie much of the recent progress on these problems.

26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th