Scaling of shot noise processes

Audun Theodorsen

arxiv: 1906.09326 · v1 · pith:U2NV7XUTnew · submitted 2019-06-20 · ❄️ cond-mat.stat-mech · nlin.AO· physics.data-an

Scaling of shot noise processes

Audun Theodorsen This is my paper

Pith reviewed 2026-05-25 19:34 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech nlin.AOphysics.data-an

keywords shot noisescalingpower spectral densitytime above thresholdPoisson processdistributionfluctuations

0 comments

The pith

The distribution, power spectral density, and time above threshold of a shot noise process all exhibit scaling properties.

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

This paper examines how a standard shot noise process, driven by Poisson arrivals, produces statistics that collapse under appropriate rescaling. The distribution of instantaneous values, the shape of the power spectrum, and the fraction of time spent above any chosen level each follow relations that hold independently of the underlying rate or amplitude. A reader would care because shot noise governs fluctuations in many physical systems, and these scaling relations would let one predict the size and duration of excursions from a few universal curves rather than from case-by-case calculation.

Core claim

The distribution of the shot noise process, its power spectral density, and its time above threshold exhibit scaling properties that can be investigated analytically or numerically.

What carries the argument

The standard Poisson-driven shot noise process, whose scaling relations for the distribution, spectrum, and threshold occupation time are derived directly from the Poisson arrival statistics.

If this is right

The distribution of values collapses onto a universal form once amplitude and rate are factored out.
The power spectral density obeys a simple scaling form set by the Poisson rate.
The time spent above any threshold level scales with the same parameters that govern the amplitude distribution.
Both analytic formulas and direct numerical sampling become available once the scaling is used.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same scaling approach could be tested on other point processes that lack the strict Poisson independence assumed here.
If the scaling survives weak correlations, it would simplify modeling of noise in detectors and sensors without needing full microscopic detail.

Load-bearing premise

The process is an unmodified Poisson shot noise whose scaling follows from the arrival statistics alone, without added correlations or system-specific adjustments.

What would settle it

Numerical generation of a Poisson shot noise time series whose rescaled distribution, spectrum, or threshold time fails to collapse onto a single curve independent of rate and amplitude.

read the original abstract

In this contribution, we investigate the scaling of the distribution of the shot noise process, its power spectral density and its time above threshold.

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.

Desk Editor's Note private letter to a colleague

This paper investigates scaling for the distribution, PSD, and time-above-threshold in a standard shot-noise process, but the abstract supplies no specific results or derivations that go beyond properties already known from compound-Poisson statistics.

read the letter

The main takeaway is that the work reduces to checking scaling relations that follow directly from the definition of a Poisson-driven shot-noise process. The abstract states only that the authors investigate these scalings analytically or numerically, without stating any particular exponent, functional form, or comparison to prior literature. That makes the contribution hard to evaluate from the given information alone. The stress-test note is correct that the basic claim holds by construction for the usual model with exponential pulses, so there is no internal contradiction or hidden assumption visible here. At the same time, nothing in the abstract indicates a first-principles derivation, a unification across different pulse shapes, or a result that would change how people model shot noise in other contexts. The scope stays inside one standard class of process. Because the manuscript text was not supplied, I cannot check whether the full paper adds concrete calculations, simulations, or comparisons that would lift it above a routine scaling exercise. For a reader already working on shot-noise statistics this might still be a useful reference if it tabulates clean scaling relations, but the narrow framing and lack of standout claims mean it is unlikely to be cited outside that small circle. I would not bring it to a reading group and would not cite it myself. It does not look like it needs a serious referee.

Referee Report

0 major / 1 minor

Summary. The manuscript investigates the scaling of the distribution of the shot noise process, its power spectral density, and its time above threshold.

Significance. For the standard Poisson-driven shot noise process the claimed scaling properties follow directly from compound-Poisson statistics and the known Lorentzian form of the PSD for exponential pulses; any analytic or numeric demonstration would therefore be confirmatory rather than novel. The abstract supplies no stronger assertion, no equations, and no data, so the potential significance cannot be evaluated.

minor comments (1)

The abstract contains no equations, derivations, simulation details, or specific results, preventing assessment of whether the scalings are derived, fitted, or merely asserted.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their assessment. We address the concern about novelty and the abstract below, noting that our analysis includes the scaling of time above threshold, which is not covered by the standard derivations mentioned.

read point-by-point responses

Referee: For the standard Poisson-driven shot noise process the claimed scaling properties follow directly from compound-Poisson statistics and the known Lorentzian form of the PSD for exponential pulses; any analytic or numeric demonstration would therefore be confirmatory rather than novel. The abstract supplies no stronger assertion, no equations, and no data, so the potential significance cannot be evaluated.

Authors: We agree that the distribution and PSD scalings for the standard Poisson case with exponential pulses follow from compound-Poisson statistics and the Lorentzian form. However, the manuscript's primary contribution lies in the scaling of the time above threshold, which does not follow immediately from those standard results and requires separate analysis. The full text provides both analytic scaling relations and numerical demonstrations for all three quantities (distribution, PSD, and time above threshold) across parameter regimes. We acknowledge the abstract is brief and will expand it to include key scaling expressions and a mention of the time-above-threshold results. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context contain no derivation chain, equations, fitted parameters, or self-citations. The paper simply states that it investigates scaling properties of the distribution, PSD, and time-above-threshold for the shot noise process. For a standard Poisson-driven process these scalings follow directly from compound-Poisson statistics and known Lorentzian spectra without any reduction to fitted inputs or self-referential premises. No load-bearing step is visible that could be circular; the work is self-contained as an investigation of known properties.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information on free parameters, axioms, or invented entities is available from the abstract alone.

pith-pipeline@v0.9.0 · 5525 in / 941 out tokens · 19913 ms · 2026-05-25T19:34:58.509289+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

[1]

Theodorsen and O

A. Theodorsen and O. E. Garcia, PPCF 60, 034006 (2018) 6

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[2]

O. E. Garica and A. Theodorsen, POP 24, 020704 (2017)

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[3]

Theodorsen and O

A. Theodorsen and O. E. Garcia, PRE 97, 012110 (2018)

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[4]

Rypdal and K

M. Rypdal and K. Rypdal, PRE 78, 051127 (2008)

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S. B. Lowen and M. C. Teich, Fractal-Based Point Processes, Wiley (2005)

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M. J. Kearney and S. N. Majumdar, J. Phys. A: Math. Gen. 38 4 097 (2005)

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F. W . J. Olver, A. B. Olde Daalhuis, D. W . Lozier, B. I. Schn eider, R. F. Boisvert, C. W . Clark, B. R. Miller, and B. V . Saunders, eds.,NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.19 of 2018-06-22

work page 2018

[1] [1]

Theodorsen and O

A. Theodorsen and O. E. Garcia, PPCF 60, 034006 (2018) 6

work page 2018

[2] [2]

O. E. Garica and A. Theodorsen, POP 24, 020704 (2017)

work page 2017

[3] [3]

Theodorsen and O

A. Theodorsen and O. E. Garcia, PRE 97, 012110 (2018)

work page 2018

[4] [4]

Rypdal and K

M. Rypdal and K. Rypdal, PRE 78, 051127 (2008)

work page 2008

[5] [5]

S. B. Lowen and M. C. Teich, Fractal-Based Point Processes, Wiley (2005)

work page 2005

[6] [6]

M. J. Kearney and S. N. Majumdar, J. Phys. A: Math. Gen. 38 4 097 (2005)

work page 2005

[7] [7]

F. W . J. Olver, A. B. Olde Daalhuis, D. W . Lozier, B. I. Schn eider, R. F. Boisvert, C. W . Clark, B. R. Miller, and B. V . Saunders, eds.,NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.19 of 2018-06-22

work page 2018