广西民族大学数学与物理学院,广西 南宁 530006
杜振叶(1996年生),男;研究方向:随机Loewner演变(SLE);E-mail:duzhenyemath@163.com
蓝师义(1966年生),男;研究方向:随机Loewner演变(SLE);E-mail:lanshiyi@gxun.edu.cn
纸质出版日期:2021-09-25,
网络出版日期:2021-03-19,
收稿日期:2020-06-18,
录用日期:2020-11-11
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杜振叶,蓝师义.偶极Loewner微分方程的一些估计[J].中山大学学报(自然科学版),2021,60(05):175-184.
DU Zhenye,LAN Shiyi.Some estimates for the dipolar Loewner differential equation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(05):175-184.
杜振叶,蓝师义.偶极Loewner微分方程的一些估计[J].中山大学学报(自然科学版),2021,60(05):175-184. DOI: 10.13471/j.cnki.acta.snus.2020.06.18.2020A027.
DU Zhenye,LAN Shiyi.Some estimates for the dipolar Loewner differential equation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(05):175-184. DOI: 10.13471/j.cnki.acta.snus.2020.06.18.2020A027.
Loewner微分方程是一种产生Loewner链的偏微分方程。首先,应用Bieberbach定理给出了偶极Loewner微分方程的解关于时间方向变化的一个估计;其次,基于逆时间的Loewner微分方程导出了对应于两个不同驱动函数的偶极Loewner微分方程的解的差值可以通过这两个驱动函数差的上确界范数来估计。这将通弦与径向Loewner微分方程的一些相应结果推广到偶极Loewner微分方程。
The Loewner differential equation is a partial differential equation that generates a Loewner chain. An estimation of the solution of the dipolar Loewner differential equation for time-direction is first derived by using Bieberbach theorem.Based on the reverse-time Loewner equation the difference of two solutions to the dipolar Loewner equation with two different deriving functions is estimated in terms of the supremum norm of the difference of the two driving functions. This generalizes some related results for the chordal and radial Loewner equations to the dipolar setting.
Loewner微分方程驱动函数随机Loewner演变(SLE)
Loewner differential equationdriving functionstochastic Loewner evolution (SLE)
SCHRAMM O. Scaling limits of loop-erased random walks and uniform spanning trees [J]. Israel J Math,2000, 118: 221-288.
CHELKAK D, HONGLER C, IZYUROV K. Conformal invariance of spin correlations in the planar Ising model [J]. Ann of Math, 2015, 181(3): 1087-1138.
CHELKAKD, SMIRNOV S. Universality in the 2D Ising model and conformal invariance of fermionic observables [J]. Invent Math, 2012, 189: 515-580.
SMIRNOV S. Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits [J]. C R Acad Sci Paris Sér I Math, 2001, 333: 239-244.
LAWLER G F, SCHRAMM O, WERNER W. Conformal invariance of planar loop-erased random walks and uniform spanning trees [J]. Ann Probab, 2004, 32: 939-995.
SCHRAMM O, SHEFFIELD S. The harmonic explorer and its convergence to SLE(4) [J]. Ann Probab, 2005, 33: 2127-2148.
SCHRAMM O, SHEFFIELD S. Contour lines of the two-dimensional discrete Gaussian free field [J]. Acta Math, 2009, 202:21-137.
SMIRNOV S. Conformal invariance in random cluster models. I. Holmorphic fermions in the Ising model [J]. Ann of Math, 2010, 172(2): 1435-1467.
LAWLER G F, SCHRAMM O, WERNER W. The dimension of the planar Brownian frontier is 4/3 [J]. Math Res Lett, 2001, 8: 401-411.
LAWLER G F, SCHRAMM O, WERNER W. Values of Brownian intersection exponents I: half-plane exponents [J]. Acta Math, 2001, 187: 237-273.
LAWLER G F, SCHRAMM O, WERNER W. Values of Brownian intersection exponents II: plane exponents [J]. Acta Math,2001, 187: 275-308.
LAWLER G F, SCHRAMM O, WERNER W. Values of Brownian intersection exponents III: two-sided exponents [J]. Ann Int Henri Poincaré, 2002, 38: 109-123.
VIKLUND F J. Convergence rates for loop-erased random walk and other Loewner curves [J]. Ann Probab, 2015,43: 119-165.
VIKLUND F J, ROHDE S, WONG C. On the continuity of <math id="M360"><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49474202&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49474214&type=6.519333363.21733332 in <math id="M361"><mi>κ</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49474216&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49474215&type=1.778000002.28600001 [J]. Probability Theory Related Fields, 2014, 159: 413-433.
LAWLER G F. Conformally invariant processes in the plane [M]. Providence, RI: American Mathematical Society, 2005.
MARSHALL D E, ROHDE S. The Loewner differential equation and slit mappings [J]. J Amer Math Soc, 2005, 18: 763-778.
李忠. 复分析导引 [M].北京: 北京大学出版社,2004.
KAGER W. NIENHUIS B. A guide to stochastic Löwner evolution and its applications [J]. J Stat Phys, 2004, 115: 1149-1229.
BAUER M, BERNARD D, HOUDAGER J. Diploar stochastic Loewner evolution [J]. J Stat Mech Theor and Exper, 2005, 3(3): 336-354.
AHLFORS L V. Complex analysis: an introduction to the theory of analytic functions of one complex variable [M]. New York: McGraw-Hill, 1966.
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