English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The following question is the subject of our work: could a two-dimensionalrandom path pushed by some constraints to an improbable "large deviationregime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang(KPZ) fluctuations? The answer is positive, though non-universal, since thefluctuations depend on the underlying geometry. We consider in details twoexamples of 2D systems for which imposed external constraints force theunderlying stationary stochastic process to stay in an atypical regime withanomalous statistics. The first example deals with the fluctuations of astretched 2D random walk above a semicircle or a triangle. In the secondexample we consider a 2D biased random walk along a channel with forbiddenvoids of circular and triangular shapes. In both cases we are interested in thedependence of a typical span $\left< d(t) \right> \sim t^{\gamma}$ of thetrajectory of $t$ steps above the top of the semicircle or the triangle. Weshow that $\gamma = \frac{1}{3}$, i.e. $\left< d(t) \right>$ shares the KPZstatistics for the semicircle, while $\gamma=0$ for the triangle. We proposeheuristic derivations of scaling exponents $\gamma$ for different geometries,justify them by explicit analytic computations and compare with numericsimulations. For practical purposes, our results demonstrate that the geometryof voids in a channel might have a crucial impact on the width of the boundarylayer and, thus, on the heat transfer in the channel.

Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime