Coupling Independence Implies Zero-Freeness 5XPM4E03W6

URI	`m2://res/5XPM4E03W6`
Kind	preprint
Creators	Shuai Shao, Ke Shi
Date	2026-10-08
Subjects	arxiv cs.DS, arxiv math-ph, arxiv math.MP, arxiv math.PR
Scope	border

Expressions

e1: version, preprint

Date	2026-10-08
Ids	arXiv 2610.12456

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Potts disc around \texorpdfstring{$z=0$}{z=0	statement	proposition 3.5	arxiv
$b$-edge covers	statement	corollary 5.9	arxiv
Coupling independence implies zero-freeness	statement	theorem 3.1	arxiv
Hamming coupling independence on \texorpdfstring{$[0,1]$}{[0,1	statement	theorem 4.1	arxiv
Complex averages under nearby laws	statement	lemma 3.2	arxiv
Soft Potts as a random hard-colouring model	statement	lemma 4.4	arxiv
The two hard instances differ only near \(v\	statement	lemma 4.8	arxiv
Conditional hard estimate	statement	proposition 4.10	arxiv
Edge-colour Lee--Yang polydisc	statement	corollary 5.4	arxiv
Finite-state continuity of normalized laws	statement	lemma 4.3	arxiv
Coupling input at \texorpdfstring{$q=11\Deg/6$}{q=11Delta/6	statement	corollary 4.13	arxiv
Lee--Yang polydisc	statement	theorem 5.2	arxiv
Soft path contraction	statement	lemma 4.11	arxiv
Potts coupling independence	definition	definition 2.2	arxiv
Stationary comparison	statement	lemma 4.2	arxiv
$b$-matchings	statement	corollary 5.7	arxiv
Coupling independence implies zero-freeness, informal	statement	theorem 1.2	arxiv
Residual Holant input	statement	lemma 5.5	arxiv
Hard list-flip transition	definition	definition 4.5	arxiv
Effect of adding one labelled free--pinned edge	statement	lemma 4.9	arxiv
Hard feasibility	statement	lemma 2.1	arxiv
Potts zero-freeness	statement	theorem 1.1	arxiv
One-vertex comparison at \texorpdfstring{$z=0$}{z=0	statement	lemma 3.4	arxiv
Log-concave Holant polytube	statement	theorem 5.6	arxiv
Positive-activity Potts induction	statement	lemma 3.3	arxiv
Vigoda-profile coupling for newly pinned laws	statement	proposition 4.12	arxiv
Soft flip kernels	statement	lemma 4.7	arxiv
Soft flip kernel	definition	definition 4.6	arxiv
Field transfer	statement	proposition 5.1	arxiv

Catalogue records

arxiv: 2610.12456 (work)

Item	Kind	Where	Source
Potts disc around \texorpdfstring{\(z=0\)}{z=0	statement	proposition 3.5	arxiv
\(b\)-edge covers	statement	corollary 5.9	arxiv
Coupling independence implies zero-freeness	statement	theorem 3.1	arxiv
Hamming coupling independence on \texorpdfstring{$[0,1]$}{[0,1	statement	theorem 4.1	arxiv
Complex averages under nearby laws	statement	lemma 3.2	arxiv
Soft Potts as a random hard-colouring model	statement	lemma 4.4	arxiv
The two hard instances differ only near \(v\	statement	lemma 4.8	arxiv
Conditional hard estimate	statement	proposition 4.10	arxiv
Edge-colour Lee--Yang polydisc	statement	corollary 5.4	arxiv
Finite-state continuity of normalized laws	statement	lemma 4.3	arxiv
Coupling input at \texorpdfstring{\(q=11\Deg/6\)}{q=11Delta/6	statement	corollary 4.13	arxiv
Lee--Yang polydisc	statement	theorem 5.2	arxiv
Soft path contraction	statement	lemma 4.11	arxiv
Potts coupling independence	definition	definition 2.2	arxiv
Stationary comparison	statement	lemma 4.2	arxiv
\(b\)-matchings	statement	corollary 5.7	arxiv
Coupling independence implies zero-freeness, informal	statement	theorem 1.2	arxiv
Residual Holant input	statement	lemma 5.5	arxiv
Hard list-flip transition	definition	definition 4.5	arxiv
Effect of adding one labelled free--pinned edge	statement	lemma 4.9	arxiv
Hard feasibility	statement	lemma 2.1	arxiv
Potts zero-freeness	statement	theorem 1.1	arxiv
One-vertex comparison at \texorpdfstring{\(z=0\)}{z=0	statement	lemma 3.4	arxiv
Log-concave Holant polytube	statement	theorem 5.6	arxiv
Positive-activity Potts induction	statement	lemma 3.3	arxiv
Vigoda-profile coupling for newly pinned laws	statement	proposition 4.12	arxiv
Soft flip kernels	statement	lemma 4.7	arxiv
Soft flip kernel	definition	definition 4.6	arxiv
Field transfer	statement	proposition 5.1	arxiv