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arxiv: 2602.07387 · v2 · submitted 2026-02-07 · ❄️ cond-mat.stat-mech

Diffusion/Subdiffusion in the Pushy Random Walk

Ofek Lauber Bonomo , Itamar Shitrit , Shlomi Reuveni , Sidney Redner This is my paper

Pith reviewed 2026-05-16 06:49 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords pushy random walksubdiffusioncrowded mediaactive particlesobstacle pushingcavity formationdiffusion transition
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0 comments X

The pith

The pushy random walk forms an obstacle-free cavity that grows subdiffusively with time in one and two dimensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper defines the pushy random walk as a process in which a single walker displaces multiple obstacles, allowing continued motion through regions of finite density. Scaling arguments and simulations show that in one dimension the walker clears a growing cavity whose length increases slower than ordinary diffusion. In two dimensions the same pushing action produces a density-driven transition: at low obstacle density the walker diffuses freely, while at high density it remains trapped inside a cavity whose radius grows subdiffusively. These results illustrate how local rearrangements induced by the walker itself alter long-term transport in crowded, deformable settings.

Core claim

We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. Using scaling arguments and numerical simulations, we show that in one dimension the walker carves out an obstacle-free cavity whose length grows subdiffusively over time. In two dimensions, increasing obstacle density drives a transition from free diffusion to localized behavior, where the walker is trapped within a cavity whose radius again grows subdiffusively with time.

What carries the argument

The pushy random walk, defined by the rule that the walker displaces any number of obstacles it encounters, thereby carving an expanding empty region.

Load-bearing premise

The unspecified pushing rules and obstacle properties in the model are sufficient to represent the interactions of real active particles with dense deformable media.

What would settle it

Track the cavity radius versus time in a controlled one- or two-dimensional experiment with mobile obstacles and test whether the growth exponent is less than one half.

Figures

Figures reproduced from arXiv: 2602.07387 by Itamar Shitrit, Ofek Lauber Bonomo, Shlomi Reuveni, Sidney Redner.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Illustration of a pushy random walk (circle) in one [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The result after a random walk in 2D pushes against [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cavity length versus time for a pushy random walk [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A cavity in two dimensions with a surrounding crust. [PITH_FULL_IMAGE:figures/full_fig_p002_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Cavity radius [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Trajectories of the pushy random walk in the diffusive [PITH_FULL_IMAGE:figures/full_fig_p003_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Main: Mean number of holes in the crust versus time [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
read the original abstract

We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions of active particles with dense, deformable media. Using scaling arguments and numerical simulations, we show that in one dimension the walker carves out an obstacle-free cavity whose length grows subdiffusively over time. In two dimensions, increasing obstacle density drives a transition from free diffusion to localized behavior, where the walker is trapped within a cavity whose radius again grows subdiffusively with time. These results show how tracer-induced rearrangements qualitatively reshape transport in crowded media and provide a minimal framework for describing diffusion in deformable environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper introduces the pushy random walk, a model in which a walker can displace multiple obstacles to penetrate dense environments. It claims, via scaling arguments and simulations, that in 1D the walker carves an obstacle-free cavity whose length grows subdiffusively with time, while in 2D increasing obstacle density induces a transition from free diffusion to localization inside a cavity whose radius grows subdiffusively.

Significance. If the claims are substantiated, the work supplies a minimal framework for tracer-induced rearrangements in crowded, deformable media and their effect on transport exponents. This could connect to experiments on active particles in biological or colloidal systems and highlight how pushing mechanics qualitatively alter diffusion.

major comments (1)
  1. [Model definition] Model definition (abstract and main text): the precise displacement rule for pushing multiple obstacles, the treatment of obstacle-obstacle interactions, and the acceptance probability are left unspecified. Because the reported subdiffusive cavity scaling is asserted to follow from these rules, the absence of an explicit algorithmic definition makes it impossible to determine whether the exponent is robust or an artifact of one particular implementation choice (e.g., sequential vs. collective pushing).
minor comments (1)
  1. [Abstract] Abstract: the statement that results are obtained 'using scaling arguments and numerical simulations' is not accompanied by any description of the simulation protocol, error estimation, or data-selection criteria, which hinders immediate assessment of the supporting evidence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting the need for greater precision in the model definition. We agree that an explicit algorithmic description is required for reproducibility and to substantiate the claimed scaling. We address this below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Model definition (abstract and main text): the precise displacement rule for pushing multiple obstacles, the treatment of obstacle-obstacle interactions, and the acceptance probability are left unspecified. Because the reported subdiffusive cavity scaling is asserted to follow from these rules, the absence of an explicit algorithmic definition makes it impossible to determine whether the exponent is robust or an artifact of one particular implementation choice (e.g., sequential vs. collective pushing).

    Authors: We agree that the initial submission did not provide a sufficiently explicit algorithmic definition of the pushing rules. In the revised manuscript we will add a dedicated Methods subsection (with pseudocode) that specifies: (i) the walker selects a lattice direction uniformly at random and attempts a unit step; (ii) any obstacle(s) lying along that ray are displaced sequentially in the same direction until free space is created for the walker (collective pushing is not implemented); (iii) obstacle-obstacle interactions are treated as hard-core exclusions with instantaneous displacement and no overlap allowed; (iv) the move is always accepted once space is created (acceptance probability = 1). We will also add a short robustness check in the supplement demonstrating that the reported subdiffusive exponents remain unchanged under modest variations of the pushing protocol (sequential vs. limited simultaneous displacement). revision: yes

Circularity Check

0 steps flagged

No circularity: new model with independent scaling and simulations

full rationale

The paper introduces the pushy random walk as a novel construct and derives subdiffusive cavity growth via scaling arguments plus numerical simulations. No derivation step reduces to a self-definition, fitted input renamed as prediction, or self-citation chain. The reported scalings are presented as consequences of the model's rules rather than tautological restatements of inputs. This is the standard non-circular case for a newly defined stochastic process analyzed by scaling and direct simulation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that obstacles can be pushed by the walker in a minimal way that captures real deformable media behavior.

axioms (1)
  • domain assumption The walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density.
    This is the core modeling choice stated in the abstract as the basis for the process.
invented entities (1)
  • Pushy random walk no independent evidence
    purpose: Minimal model for active particle interactions with dense deformable media
    Newly defined process introduced in the abstract without external validation details.

pith-pipeline@v0.9.0 · 5423 in / 1282 out tokens · 45308 ms · 2026-05-16T06:49:47.036618+00:00 · methodology

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Reference graph

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