Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variance limite d'une marche al\'eatoire r\'eversible en milieu
  al\'eatoire sur Z (Limit of the Variance of a Reversible Random Walk in
  Random Medium on Z)   The Central Limit Theorem for the random walk on a stationary random network
of conductances has been studied by several authors. In one dimension, when
conductances and resistances are integrable, and following a method of
martingale introduced by S. Kozlov (1985), we can prove the Quenched Central
Limit Theorem. In that case the variance of the limit law is not null. When
resistances are not integrable, the Annealed Central Limit Theorem with null
variance was established by Y. Derriennic and M. Lin (personal communication).
The quenched version of this last theorem is proved here, by using a very
simple method. The similar problem for the continuous diffusion is then
considered. Finally our method allows us to prove an inequality for the
quadratic mean of a diffusion (X_t)_t at all time t.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con