# Scaling limits for sub-ballistic biased random walks in random conductances

Source: [Scaling limits for sub-ballistic biased random walks in random conductances](<https://www.sota2.com/research/paper/68fa531f1e209131ce980b88>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:17:07.273Z

Authors: Alexander Fribergh, Daniel Kious

Published: 2016-01-05T16:23:10.000Z

## Abstract

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of Large Numbers for the position of the walker, properly rescaled. Moreover, we state a functional Central Limit Theorem where an atypical process, related to the Fractional Kinetics, appears in the limit.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1601.00889>)

[PDF](<https://arxiv.org/pdf/1601.00889.pdf>)