Does a twin fitted to the sensor-delay histogram certify gains that bursty delay makes unstable?

research/jitter-twin

A twin fitted to the sensor-delay histogram is blind to its persistence: i.i.d. jitter at the mean delay barely moves the mean-square gain limit (1.00 for {0,2}), but with the marginal fixed, lag-1 autocorrelation 0.9 cuts it to 0.67 (0.9 certified by the twin is unstable from ρ=0.435) and inflates variance 2.4×; almost-sure stability (≈1.84) hides it.

8 tests

What it found

Scalar loop x[n+1]=x[n]−k x[n−d_n]+w[n] with random delay; the twin has the same marginal delay law (constant mean: stable iff k<2 sin(π/(2(2d+1)))). Independent jitter moves the mean-square limit little and in either direction (1.000 for {0,2}, 0.952 for {0,1,2}, 0.668 vs the twin’s 0.618 for {0,1,2,3,4}); for {0,2} with P(d=2)=p it fits k(k+1)=1/p. Persistence, invisible in the histogram, is the large effect: at fixed marginal the limit falls 1.000→0.875→0.672→0.624 at lag-1 autocorrelation ρ=0, 0.5, 0.9, 0.99 (towards the worst-case constant delay’s 0.618); a twin-certified k=0.9 is unstable from ρ=0.435, and below the limit the variance at k=0.6 inflates from 2.56 to 6.26 (ρ=0.9) and 15.2 (ρ=0.99). Almost-sure stability (simulated limit ≈1.84) is insensitive to ρ, so which stability the safety claim needs decides whether persistence matters. Companion to the latency twin. Stylised: scalar plant, sticky-redraw delay, Monte-Carlo almost-sure limits (one seed).

A figure from its own output

Figure produced by research/jitter-twin: threshold_vs_delay — jitter-twin/experiments/threshold_vs_delay.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.