Pith Number

pith:3OHNMBEQ

pith:2026:3OHNMBEQBJBRR3JTFHW5DIA6MX

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Resetting-induced instability in queues fed by a search process in an interval

Jos\'e Giral-Barajas, Paul C. Bressloff

Stochastic resetting in search processes feeding queues exhibits a threshold rate that reverses its impact on convergence to steady state, growing exponentially with the number of servers.

arxiv:2602.05009 v2 · 2026-02-04 · cond-mat.stat-mech

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Claims

C1strongest claim

We find a threshold resetting rate at which the effects of stochastic resetting shift from reducing convergence regions to expanding them. Furthermore, we demonstrate that this threshold value grows exponentially with the number of servers.

C2weakest assumption

That the steady-state conditions derived separately from queuing theory and from resetting search processes in a bounded domain can be combined directly without additional coupling terms or approximation errors that would alter the location of the threshold.

C3one line summary

Stochastic resetting in bounded search processes that feed queues creates a threshold rate beyond which it expands rather than shrinks steady-state convergence regions, with the threshold growing exponentially in the number of servers.

References

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[1] Another topic of current interest is search processes with stochastic resetting [ 26]

[2] (5) Therefore, all the quantities of interest for the search process can be described via the Laplace transform of the probability ﬂux into the target, ˜J0(x0,s )

[3] yields ˜F0(s) = ˜f0(s) ˜ϕ (s). (10) B. Convergence zones for the G/M/c without resetting As highlighted in the introduction, the accumulation of resources after several rounds of the search-and-captur

[4] ( 7b) to derive the follow- ing condition for convergence to a steady-state number of resources [ 20]: x0 >x ∗ 0 where x∗ 0 =L − √ L2 − 2D cµ + 2Dτcap

[5] Stochastic resetting has been 5 FIG. 2. Critical spatial conﬁgurations for the existence of a steady-state distribution with instantaneous refractor y periods. (a) The threshold starting position of t

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Receipt and verification

First computed	2026-05-20T00:00:33.602669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db8ed604900a4318ed3329edd1a01e65e8fe8022dfda3cf65ee1e2613fe2f60f

Aliases

arxiv: 2602.05009 · arxiv_version: 2602.05009v2 · doi: 10.48550/arxiv.2602.05009 · pith_short_12: 3OHNMBEQBJBR · pith_short_16: 3OHNMBEQBJBRR3JT · pith_short_8: 3OHNMBEQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3OHNMBEQBJBRR3JTFHW5DIA6MX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: db8ed604900a4318ed3329edd1a01e65e8fe8022dfda3cf65ee1e2613fe2f60f

Canonical record JSON

{
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    "abstract_canon_sha256": "18f3040a8be21a14ba1613f7002ce7ddfd9025a64ac151224262a48b37347ec9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-02-04T19:52:10Z",
    "title_canon_sha256": "f9e19054fea6ca567aa6de359b69be1ec39cf8ad16f62401d7fa8f7004e2fd8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.05009",
    "kind": "arxiv",
    "version": 2
  }
}