Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $
Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it b...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kennedy, Tom [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of statistical physics - Springer US, 1969, 146(2011), 2 vom: 02. Dez., Seite 281-293 |
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| Übergeordnetes Werk: |
volume:146 ; year:2011 ; number:2 ; day:02 ; month:12 ; pages:281-293 |
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| DOI / URN: |
10.1007/s10955-011-0406-5 |
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OLC2046617959 |
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| 520 | |a Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. | ||
| 650 | 4 | |a 2d self-avoiding walk | |
| 650 | 4 | |a Radial SLE | |
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10.1007/s10955-011-0406-5 doi (DE-627)OLC2046617959 (DE-He213)s10955-011-0406-5-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kennedy, Tom verfasserin aut Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2011 Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. 2d self-avoiding walk Radial SLE Fixed length Enthalten in Journal of statistical physics Springer US, 1969 146(2011), 2 vom: 02. Dez., Seite 281-293 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:146 year:2011 number:2 day:02 month:12 pages:281-293 https://doi.org/10.1007/s10955-011-0406-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4323 33.00 VZ AR 146 2011 2 02 12 281-293 |
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10.1007/s10955-011-0406-5 doi (DE-627)OLC2046617959 (DE-He213)s10955-011-0406-5-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kennedy, Tom verfasserin aut Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2011 Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. 2d self-avoiding walk Radial SLE Fixed length Enthalten in Journal of statistical physics Springer US, 1969 146(2011), 2 vom: 02. Dez., Seite 281-293 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:146 year:2011 number:2 day:02 month:12 pages:281-293 https://doi.org/10.1007/s10955-011-0406-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4323 33.00 VZ AR 146 2011 2 02 12 281-293 |
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10.1007/s10955-011-0406-5 doi (DE-627)OLC2046617959 (DE-He213)s10955-011-0406-5-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kennedy, Tom verfasserin aut Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2011 Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. 2d self-avoiding walk Radial SLE Fixed length Enthalten in Journal of statistical physics Springer US, 1969 146(2011), 2 vom: 02. Dez., Seite 281-293 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:146 year:2011 number:2 day:02 month:12 pages:281-293 https://doi.org/10.1007/s10955-011-0406-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4323 33.00 VZ AR 146 2011 2 02 12 281-293 |
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10.1007/s10955-011-0406-5 doi (DE-627)OLC2046617959 (DE-He213)s10955-011-0406-5-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kennedy, Tom verfasserin aut Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2011 Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. 2d self-avoiding walk Radial SLE Fixed length Enthalten in Journal of statistical physics Springer US, 1969 146(2011), 2 vom: 02. Dez., Seite 281-293 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:146 year:2011 number:2 day:02 month:12 pages:281-293 https://doi.org/10.1007/s10955-011-0406-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4323 33.00 VZ AR 146 2011 2 02 12 281-293 |
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10.1007/s10955-011-0406-5 doi (DE-627)OLC2046617959 (DE-He213)s10955-011-0406-5-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kennedy, Tom verfasserin aut Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2011 Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. 2d self-avoiding walk Radial SLE Fixed length Enthalten in Journal of statistical physics Springer US, 1969 146(2011), 2 vom: 02. Dez., Seite 281-293 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:146 year:2011 number:2 day:02 month:12 pages:281-293 https://doi.org/10.1007/s10955-011-0406-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4323 33.00 VZ AR 146 2011 2 02 12 281-293 |
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Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. © Springer Science+Business Media, LLC 2011 |
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Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. © Springer Science+Business Media, LLC 2011 |
| abstract_unstemmed |
Abstract We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial $ SLE_{8/3} $ in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial $ SLE_{8/3} $. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial $ SLE_{8/3} $, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values. © Springer Science+Business Media, LLC 2011 |
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| title_short |
Transforming Fixed-Length Self-avoiding Walks into Radial $ SLE_{8/3} $ |
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https://doi.org/10.1007/s10955-011-0406-5 |
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