Pith Number

pith:5SWCIA7E

pith:2026:5SWCIA7EMTHCG24YUUOZYPHTXK

not attested not anchored not stored refs pending

A pluricomplex error-function kernel at the edge of polynomial Bergman kernels

L. D. Molag

Near the droplet edge, polynomial Bergman kernels converge locally to the error-function kernel or a new multivariate version of it.

arxiv:2604.04661 v3 · 2026-04-06 · math.PR · math-ph · math.CV · math.MP

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Claims

C1strongest claim

We show that the local behavior of the kernel in the vicinity of the edge ∂S_Q is described in two different ways by universal limiting kernels. One of these limiting kernels is the error-function kernel, which is ubiquitous in random matrix theory, while the other limiting kernel is a new universal object: a multivariate version of the error-function kernel.

C2weakest assumption

The results hold under mild conditions on the potential Q and only in the two qualitatively different settings: (i) the tensorized case where Q decomposes as a sum of planar potentials, and (ii) the case where Q is rotational symmetric.

C3one line summary

At the edge of droplets for polynomial Bergman kernels, local statistics are described by the error-function kernel and a new multivariate error-function kernel in tensorized or rotationally symmetric settings.

Receipt and verification

First computed	2026-05-20T00:05:44.344726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecac2403e464ce236b98a51d9c3cf3baaec4e694973f4a43c2c26441d6a6a051

Aliases

arxiv: 2604.04661 · arxiv_version: 2604.04661v3 · doi: 10.48550/arxiv.2604.04661 · pith_short_12: 5SWCIA7EMTHC · pith_short_16: 5SWCIA7EMTHCG24Y · pith_short_8: 5SWCIA7E

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5SWCIA7EMTHCG24YUUOZYPHTXK \
  | 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: ecac2403e464ce236b98a51d9c3cf3baaec4e694973f4a43c2c26441d6a6a051

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6054531295ba80dd117f8ae416f626a0acb4d87da82b1dbcc953f4495a29a509",
    "cross_cats_sorted": [
      "math-ph",
      "math.CV",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-06T13:15:28Z",
    "title_canon_sha256": "0c1e6740f37dd793dcdf9f426af169dd3130b342f7e783e480d063442595d7f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.04661",
    "kind": "arxiv",
    "version": 3
  }
}