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Self-Avoiding Walks on the UIPQ
Self-Avoiding Walks on the UIPQ
We study an annealed model of Uniform Infinite Planar Quadrangulation (UIPQ) with an infinite two-sided self-avoiding walk (SAW), which can also be described as the result of glueing together two independent uniform infinite quadrangulations of the half-plane (UIHPQs). We prove a lower bound on the displacement of the SAW which, combined with the estimates of [15], shows that the self-avoiding walk is diffusive. As a byproduct this implies that the volume growth exponent of the lattice in question is 4 (as is the case for the standard UIPQ); nevertheless, using our previous work [9] we show its law to be singular with respect to that of the standard UIPQ, that is – in the language of statistical physics – the fact that disorder holds.
- Université Paris Diderot France
- University of Paris-Saclay France
- Scuola Normale Superiore di Pisa Italy
- University of Bath United Kingdom
Microsoft Academic Graph classification: Pure mathematics Upper and lower bounds Combinatorics Planar Volume growth Lattice (order) Exponent Self-avoiding walk Mathematics
ACM Computing Classification System: ComputingMilieux_MISCELLANEOUS
Peeling proce, Random planar map, Settore MAT/06 - Probabilita' e Statistica Matematica, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Uniform Infinite Planar Quadrangulation, Self-avoiding walk, [MATH]Mathematics [math]
Peeling proce, Random planar map, Settore MAT/06 - Probabilita' e Statistica Matematica, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Uniform Infinite Planar Quadrangulation, Self-avoiding walk, [MATH]Mathematics [math]
Microsoft Academic Graph classification: Pure mathematics Upper and lower bounds Combinatorics Planar Volume growth Lattice (order) Exponent Self-avoiding walk Mathematics
ACM Computing Classification System: ComputingMilieux_MISCELLANEOUS
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!- Université Paris Diderot France
- University of Paris-Saclay France
- Scuola Normale Superiore di Pisa Italy
- University of Bath United Kingdom
We study an annealed model of Uniform Infinite Planar Quadrangulation (UIPQ) with an infinite two-sided self-avoiding walk (SAW), which can also be described as the result of glueing together two independent uniform infinite quadrangulations of the half-plane (UIHPQs). We prove a lower bound on the displacement of the SAW which, combined with the estimates of [15], shows that the self-avoiding walk is diffusive. As a byproduct this implies that the volume growth exponent of the lattice in question is 4 (as is the case for the standard UIPQ); nevertheless, using our previous work [9] we show its law to be singular with respect to that of the standard UIPQ, that is – in the language of statistical physics – the fact that disorder holds.