2019
DOI: 10.1103/physreve.99.012110
|View full text |Cite
|
Sign up to set email alerts
|

Anomalous one-dimensional fluctuations of a simple two-dimensional random walk in a large-deviation regime

Abstract: The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ) fluctuations?The answer is positive, though non-universal, since the fluctuations depend on the underlying geometry. We consider in details two examples of 2D systems for which imposed external constraints force the underlying stationary stochastic process to stay in an atypical regi… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

4
39
0

Year Published

2019
2019
2025
2025

Publication Types

Select...
6

Relationship

1
5

Authors

Journals

citations
Cited by 28 publications
(43 citation statements)
references
References 27 publications
4
39
0
Order By: Relevance
“…in the critical regime, where we expect that the methods developed for fermions in [71,72] will be useful. Another classical problem is the one of a single Brownian walker conditioned to remain below a circle [73][74][75]. Our calculation for N Brownian walkers under the barrier g(τ ) = W τ (1 − τ /T ) is thus a generalization of that problem.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…in the critical regime, where we expect that the methods developed for fermions in [71,72] will be useful. Another classical problem is the one of a single Brownian walker conditioned to remain below a circle [73][74][75]. Our calculation for N Brownian walkers under the barrier g(τ ) = W τ (1 − τ /T ) is thus a generalization of that problem.…”
Section: Discussionmentioning
confidence: 99%
“…Let us compute the half-space integrals for the system with a hard wall in W = 0, which are needed for the perturbative expansion around W = 0 in Eq. (74) in the text, namely…”
Section: Discussionmentioning
confidence: 99%
“…The question to be answered behind this formal relation is as follows: could we see a Griffiths-like behavior (4.2) of the partition function in the regime which we have described above? We provide some arguments, using recent results derived in [48][49][50] concerning the KPZ scaling of fluctuations in the restricted random walks on the plane. To justify the Griffiths-like behavior we first regard the model A of restricted random walk of fixed length, L, where the relation between the length, L, and the cutoff scale, R, is imposed by hands.…”
Section: Jhep04(2021)080mentioning
confidence: 99%
“…Statistics in such a tiny subset of a Gaussian ensemble is controlled by a collective behavior of strongly correlated modes, thus, for some geometries one might expect extreme distribution with a scaling different from the Gaussian. Let us briefly reproduce the arguments of the work [50]. Typically, an elongated path follows the stretching direction as much as possible, and gets curved only if curving cannot be avoided.…”
Section: Jhep04(2021)080mentioning
confidence: 99%
“…In the recent series of papers [2,3,4,5], S.Nechaev and co-authors suggested an unexpected and possibly deep mathematical connection between these two realms. Specifically, they considered the problem of a random walk on the plane outside of an excluded round disk conditioned on returning back to the starting point after specified time t and making exactly one (or any specified larger number) of turns around the obstacle.…”
Section: R ∆mentioning
confidence: 99%