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Celebratio Mathematica

Horng-Tzer Yau


Bibliography

[1]M. Loss and H.-T. Yau: “Sta­bilty of Cou­lomb sys­tems with mag­net­ic fields. III. Zero en­ergy bound states of the Pauli op­er­at­or,” Comm. Math. Phys. 104 : 2 (1986), pp. 283–​290. MR 836005

[2]E. H. Lieb and H.-T. Yau: “The Chandrasekhar the­ory of stel­lar col­lapse as the lim­it of quantum mech­an­ics,” Comm. Math. Phys. 112 : 1 (1987), pp. 147–​174. MR 904142 Zbl 0641.​35065

[3]E. H. Lieb and H.-T. Yau: “Many-body sta­bil­ity im­plies a bound on the fine-struc­ture con­stant,” Phys. Rev. Lett. 61 : 15 (1988), pp. 1695–​1697. MR 961589

[4]J. G. Con­lon, E. H. Lieb, and H.-T. Yau: “The \( N^{7/5} \) law for charged bo­sons,” Comm. Math. Phys. 116 : 3 (1988), pp. 417–​448. MR 937769

[5]E. H. Lieb and H.-T. Yau: “The sta­bil­ity and in­stabil­ity of re­lativ­ist­ic mat­ter,” Comm. Math. Phys. 118 : 2 (1988), pp. 177–​213. MR 956165 Zbl 0686.​35099

[6]H.-T. Yau: “Sta­bil­ity and in­stabil­ity of Cou­lomb and grav­it­at­ing sys­tems,” pp. 317–​319 in IXth In­ter­na­tion­al Con­gress on Math­em­at­ic­al Phys­ics (Swansea, 1988). Hil­ger (Bris­tol), 1989. MR 1033785

[7]H.-T. Yau: “Sta­bil­ity of re­lativ­ist­ic Cou­lomb and grav­it­at­ing sys­tems,” pp. 444–​458 in Schrödinger op­er­at­ors (Sønder­borg, 1988). Lec­ture Notes in Phys. 345. Spring­er (Ber­lin), 1989. MR 1037328 Zbl 0727.​35103

[8]J. G. Con­lon, E. H. Lieb, and H.-T. Yau: “The Cou­lomb gas at low tem­per­at­ure and low dens­ity,” Comm. Math. Phys. 125 : 1 (1989), pp. 153–​180. MR 1017745 Zbl 0682.​76066

[9]D. Bry­dges and H.-T. Yau: “Grad \( \phi \) per­turb­a­tions of mass­less Gaus­si­an fields,” Comm. Math. Phys. 129 : 2 (1990), pp. 351–​392. MR 1048698 Zbl 0705.​60101

[10]H.-T. Yau: “Re­l­at­ive en­tropy and hy­dro­dynam­ics of Gin­zburg–Land­au mod­els,” Lett. Math. Phys. 22 : 1 (1991), pp. 63–​80. MR 1121850

[11]C. C. Chang and H.-T. Yau: “Fluc­tu­ations of one-di­men­sion­al Gin­zburg–Land­au mod­els in nonequi­lib­ri­um,” Comm. Math. Phys. 145 : 2 (1992), pp. 209–​234. MR 1162798 Zbl 0754.​76006

[12]H.-T. Yau: “De­riv­a­tion of the Euler equa­tion from Hamilto­ni­an sys­tems with neg­li­gible ran­dom noise,” pp. 360–​363 in Math­em­at­ic­al phys­ics, X (Leipzig, 1991). Spring­er (Ber­lin), 1992. MR 1386428 Zbl 0947.​82507

[13]S. Olla, S. R. S. Varadhan, and H.-T. Yau: “Hy­dro­dynam­ic­al lim­it for a Hamilto­ni­an sys­tem with weak noise,” Comm. Math. Phys. 155 : 3 (1993), pp. 523–​560. MR 1231642 Zbl 0781.​60101 article

[14]S. L. Lu and H.-T. Yau: “Spec­tral gap and log­ar­ithmic So­bolev in­equal­ity for Kawa­saki and Glauber dy­nam­ics,” Comm. Math. Phys. 156 : 2 (1993), pp. 399–​433. MR 1233852 Zbl 0779.​60078

[15]R. Es­posito, R. Marra, and H. T. Yau: “Dif­fus­ive lim­it of asym­met­ric simple ex­clu­sion,” pp. 451–​489 in The state of mat­ter (Copen­ha­gen, 1992). Adv. Ser. Math. Phys. 20. World Sci. Publ. (River Edge, NJ), 1994. MR 1462153

[16]H.-T. Yau: “Meta­sta­bil­ity of Gin­zburg–Land­au mod­el with a con­ser­va­tion law,” J. Stat­ist. Phys. 74 : 3–​4 (1994), pp. 705–​742. MR 1263386 Zbl 0834.​35120

[17]R. Es­posito, R. Marra, and H.-T. Yau: “Dif­fus­ive lim­it of asym­met­ric simple ex­clu­sion,” pp. 1233–​1267 in Spe­cial is­sue ded­ic­ated to El­li­ott H. Lieb, published as Rev. Math. Phys. 6 : 5A (1994). MR 1301374 Zbl 0841.​60082

[18]C. Land­im and H.-T. Yau: “Large de­vi­ations of in­ter­act­ing particle sys­tems in in­fin­ite volume,” Comm. Pure Ap­pl. Math. 48 : 4 (1995), pp. 339–​379. MR 1324406 Zbl 0822.​60092

[19]T. Fun­aki, K. Uchiyama, and H. T. Yau: “Hy­dro­dynam­ic lim­it for lat­tice gas re­vers­ible un­der Bernoulli meas­ures,” pp. 1–​40 in Non­lin­ear stochast­ic PDEs (Min­neapol­is, MN, 1994). IMA Vol. Math. Ap­pl. 77. Spring­er (New York), 1996. MR 1395890 Zbl 0840.​60091

[20]C. Land­im, S. Olla, and H. T. Yau: “Some prop­er­ties of the dif­fu­sion coef­fi­cient for asym­met­ric simple ex­clu­sion pro­cesses,” Ann. Probab. 24 : 4 (1996), pp. 1779–​1808. MR 1415229 Zbl 0872.​60078

[21]R. Es­posito, R. Marra, and H. T. Yau: “Navi­er–Stokes equa­tions for stochast­ic particle sys­tems on the lat­tice,” Comm. Math. Phys. 182 : 2 (1996), pp. 395–​456. MR 1447299 Zbl 0868.​60079

[22]H.-T. Yau: “Log­ar­ithmic So­bolev in­equal­ity for lat­tice gases with mix­ing con­di­tions,” Comm. Math. Phys. 181 : 2 (1996), pp. 367–​408. MR 1414837 Zbl 0864.​60079

[23]R. Es­posito, R. Marra, and H. T. Yau: “Er­rat­um: ‘Dif­fus­ive lim­it of asym­met­ric simple ex­clu­sion’,” Rev. Math. Phys. 8 : 6 (1996), pp. 905. MR 1412360

[24]R. Es­posito, R. Marra, and H. T. Yau: “Navi­er–Stokes equa­tions for stochast­ic lat­tice gases,” Phys. Rev. E (3) 53 : 5, part A (1996), pp. 4486–​4489. MR 1388943

[25]S. R. S. Varadhan and H. T. Yau: “Scal­ing lim­its for lat­tice gas mod­els,” pp. 39–​43 in Stochast­ic pro­cesses and func­tion­al ana­lys­is (River­side, CA, Novem­ber 18–20, 1994). Edi­ted by J. A. Gold­stein, N. E. Gret­sky, and J. J. Uhl. Lec­ture Notes in Pure and Ap­plied Math­em­at­ics 186. Dek­ker (New York), 1997. MR 1440413 Zbl 0884.​60090 incollection

[26]S. R. S. Varadhan and H.-T. Yau: “Dif­fus­ive lim­it of lat­tice gas with mix­ing con­di­tions,” Asi­an J. Math. 1 : 4 (December 1997), pp. 623–​678. MR 1621569 Zbl 0947.​60089 article

[27]C. Land­im and H. T. Yau: “Fluc­tu­ation-dis­sip­a­tion equa­tion of asym­met­ric simple ex­clu­sion pro­cesses,” Probab. The­ory Re­lated Fields 108 : 3 (1997), pp. 321–​356. MR 1465163

[28]C. Land­im, S. Olla, and H. T. Yau: “First-or­der cor­rec­tion for the hy­dro­dynam­ic lim­it of asym­met­ric simple ex­clu­sion pro­cesses in di­men­sion \( d\geq3 \),” Comm. Pure Ap­pl. Math. 50 : 2 (1997), pp. 149–​203. MR 1426710 Zbl 0866.​76003

[29]H.-T. Yau: “Log­ar­ithmic So­bolev in­equal­ity for gen­er­al­ized simple ex­clu­sion pro­cesses,” Probab. The­ory Re­lated Fields 109 : 4 (1997), pp. 507–​538. MR 1483598 Zbl 0903.​60087

[30]J. Quastel and H.-T. Yau: “Lat­tice gases, large de­vi­ations, and the in­com­press­ible Navi­er–Stokes equa­tions,” Ann. of Math. (2) 148 : 1 (1998), pp. 51–​108. MR 1652971

[31]L. Erdős and H.-T. Yau: “Lin­ear Boltzmann equa­tion as scal­ing lim­it of quantum Lorentz gas,” pp. 137–​155 in Ad­vances in dif­fer­en­tial equa­tions and math­em­at­ic­al phys­ics (At­lanta, GA, 1997). Con­temp. Math. 217. Amer. Math. Soc. (Provid­ence, RI), 1998. MR 1605282

[32]C. Land­im, S. Olla, and H. T. Yau: “Con­vec­tion-dif­fu­sion equa­tion with space-time er­god­ic ran­dom flow,” Probab. The­ory Re­lated Fields 112 : 2 (1998), pp. 203–​220. MR 1653837 Zbl 0914.​60070

[33]H.-T. Yau: “Scal­ing lim­it of particle sys­tems, in­com­press­ible Navi­er–Stokes equa­tion and Boltzmann equa­tion,” pp. 193–​202 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Ber­lin, 1998), published as Doc. Math. III : Extra Vol. III (1998). MR 1648154 Zbl 0906.​60076

[34]T.-Y. Lee and H.-T. Yau: “Log­ar­ithmic So­bolev in­equal­ity for some mod­els of ran­dom walks,” Ann. Probab. 26 : 4 (1998), pp. 1855–​1873. MR 1675008 Zbl 0943.​60062

[35]E. Jan­vresse, C. Land­im, J. Quastel, and H. T. Yau: “Re­lax­a­tion to equi­lib­ri­um of con­ser­vat­ive dy­nam­ics. I: Zero-range pro­cesses,” Ann. Probab. 27 : 1 (1999), pp. 325–​360. MR 1681098

[36]L. Jensen and H.-T. Yau: “Hy­dro­dynam­ic­al scal­ing lim­its of simple ex­clu­sion mod­els,” pp. 167–​225 in Prob­ab­il­ity the­ory and ap­plic­a­tions (Prin­ceton, NJ, 1996). IAS/Park City Math. Ser. 6. Amer. Math. Soc. (Provid­ence, RI), 1999. MR 1678309 Zbl 1069.​60503

[37]J. Quastel and H.-T. Yau: “Fluc­tu­ation-dis­sip­a­tion equa­tion and in­com­press­ible Navi­er-Stokes equa­tions,” pp. 120–​130 in XIIth In­ter­na­tion­al Con­gress of Math­em­at­ic­al Phys­ics: ICMP ’97 (Bris­bane). Int. Press (Cam­bridge, MA), 1999. MR 1697269

[38]H.-T. Yau: “Asymp­tot­ic solu­tions to dy­nam­ics of many-body sys­tems and clas­sic­al con­tinuum equa­tions,” pp. 155–​236 in Cur­rent de­vel­op­ments in math­em­at­ics, 1998 (Cam­bridge, MA). Int. Press (Somerville, MA), 1999. MR 1772325 Zbl 1036.​82500

[39]S. Se­th­ura­man, S. R. S. Varadhan, and H.-T. Yau: “Dif­fus­ive lim­it of a tagged particle in asym­met­ric simple ex­clu­sion pro­cesses,” Comm. Pure Ap­pl. Math. 53 : 8 (August 2000), pp. 972–​1006. MR 1755948 Zbl 1029.​60084 article

[40]J. Fröhlich, T.-P. Tsai, and H.-T. Yau: “On a clas­sic­al lim­it of quantum the­ory and the non-lin­ear Hartree equa­tion,” pp. 57–​78 in GAFA 2000 (Tel Aviv, 1999), published as Geom. Funct. Anal. Special Volume, Part I (2000). MR 1826249

[41]H.-T. Yau: “Quantum mech­an­ics, lin­ear Boltzmann equa­tion and renor­mal­iz­a­tion,” pp. 131–​141 in Hy­dro­dynam­ic lim­its and re­lated top­ics (Toronto, ON, 1998). Fields Inst. Com­mun. 27. Amer. Math. Soc. (Provid­ence, RI), 2000. MR 1798649 Zbl 1060.​82510

[42]L. Erdős and H.-T. Yau: “Lin­ear Boltzmann equa­tion as the weak coup­ling lim­it of a ran­dom Schrödinger equa­tion,” Comm. Pure Ap­pl. Math. 53 : 6 (2000), pp. 667–​735. MR 1744001

[43]J. Fröhlich, T.-P. Tsai, and H.-T. Yau: “On a clas­sic­al lim­it of quantum the­ory and the non-lin­ear Hartree equa­tion,” pp. 189–​207 in Conférence Moshé Flato 1999 (Di­jon), vol. I. Math. Phys. Stud. 21. Kluwer Acad. Publ. (Dordrecht), 2000. MR 1805891

[44]Prizes in math­em­at­ic­al phys­ics,” pp. xv–​xxv in XIIIth In­ter­na­tion­al Con­gress on Math­em­at­ic­al Phys­ics: Laur­eates and cita­tions, ad­dresses and present­a­tions (Lon­don, 2000). Int. Press, Bo­ston, 2001. MR 1883290

[45]L. Erdős and H.-T. Yau: “De­riv­a­tion of the non­lin­ear Schrödinger equa­tion from a many body Cou­lomb sys­tem,” Adv. The­or. Math. Phys. 5 : 6 (2001), pp. 1169–​1205. MR 1926667

[46]H.-T. Yau: “Scal­ing lim­it of particle sys­tems, in­com­press­ible Navi­er–Stokes equa­tion and Boltzmann equa­tion,” pp. 171–​183 in First In­ter­na­tion­al Con­gress of Chinese Math­em­aticians (Beijing, 1998). AMS/IP Stud. Adv. Math. 20. Amer. Math. Soc. (Provid­ence, RI), 2001. MR 1830173 Zbl 1211.​82040

[47]H.-T. Yau: “Quantum dy­nam­ics of many-body sys­tems,” pp. 255–​270 in High­lights of math­em­at­ic­al phys­ics (Lon­don, 2000). Amer. Math. Soc. (Provid­ence, RI), 2002. MR 2001584 Zbl 1140.​82316

[48]B. Nachter­gaele and H.-T. Yau: “De­riv­a­tion of the Euler equa­tions from many-body quantum mech­an­ics,” pp. 467–​476 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Beijing, 2002), vol. III. High­er Ed. Press (Beijing), 2002. MR 1957554 Zbl 1001.​82069

[49]C. Bardos, L. Erdős, F. Golse, N. Maus­er, and H.-T. Yau: “De­riv­a­tion of the Schrödinger–Pois­son equa­tion from the quantum \( N \)-body prob­lem,” C. R. Math. Acad. Sci. Par­is 334 : 6 (2002), pp. 515–​520. MR 1890644

[50]T.-P. Tsai and H.-T. Yau: “Clas­si­fic­a­tion of asymp­tot­ic pro­files for non­lin­ear Schrödinger equa­tions with small ini­tial data,” Adv. The­or. Math. Phys. 6 : 1 (2002), pp. 107–​139. MR 1992875 Zbl 1033.​81034

[51]C. Land­im, G. Pan­izo, and H. T. Yau: “Spec­tral gap and log­ar­ithmic So­bolev in­equal­ity for un­boun­ded con­ser­vat­ive spin sys­tems,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 38 : 5 (2002), pp. 739–​777. MR 1931585 Zbl 1022.​60087

[52]T.-P. Tsai and H.-T. Yau: “Re­lax­a­tion of ex­cited states in non­lin­ear Schrödinger equa­tions,” Int. Math. Res. Not. 2002 : 31 (2002), pp. 1629–​1673. MR 1916427 Zbl 1011.​35120

[53]T.-P. Tsai and H.-T. Yau: “Asymp­tot­ic dy­nam­ics of non­lin­ear Schrödinger equa­tions: res­on­ance-dom­in­ated and dis­per­sion-dom­in­ated solu­tions,” Comm. Pure Ap­pl. Math. 55 : 2 (2002), pp. 153–​216. MR 1865414 Zbl 1031.​35137

[54]T.-P. Tsai and H.-T. Yau: “Stable dir­ec­tions for ex­cited states of non­lin­ear Schrödinger equa­tions,” Comm. Par­tial Dif­fer­en­tial Equa­tions 27 : 11–​12 (2002), pp. 2363–​2402. MR 1944033 Zbl 1021.​35113

[55]J. Fröhlich, T.-P. Tsai, and H.-T. Yau: “On the point-particle (New­to­ni­an) lim­it of the non-lin­ear Hartree equa­tion,” Comm. Math. Phys. 225 : 2 (2002), pp. 223–​274. MR 1889225

[56]C. Land­im and H. T. Yau: “Con­ver­gence to equi­lib­ri­um of con­ser­vat­ive particle sys­tems on \( \mathbb Z^d \),” Ann. Probab. 31 : 1 (2003), pp. 115–​147. MR 1959788 Zbl 1015.​60098

[57]B. Nachter­gaele and H.-T. Yau: “De­riv­a­tion of the Euler equa­tions from quantum dy­nam­ics,” Comm. Math. Phys. 243 : 3 (2003), pp. 485–​540. MR 2029364 Zbl 1079.​82008

[58]Lec­tures on par­tial dif­fer­en­tial equa­tions (Hsin­chu, Septem­ber 2000). Edi­ted by S.-Y. A. Chang, C.-S. Lim, and H.-T. Yau. New Stud­ies in Ad­vanced Math­em­at­ics 2. In­ter­na­tion­al Press (Somerville, MA), 2003. MR 2054270

[59]H.-T. Yau: “\( (\log t)^{2/3} \) law of the two di­men­sion­al asym­met­ric simple ex­clu­sion pro­cess,” Ann. of Math. (2) 159 : 1 (2004), pp. 377–​405. MR 2052358 Zbl 1060.​60099

[60]H.-T. Yau: “Su­per­dif­fu­sion of the asym­met­ric simple ex­clu­sion pro­cess,” pp. 147–​152 in Second In­ter­na­tion­al Con­gress of Chinese Math­em­aticians. New Stud. Adv. Math. 4. Int. Press (Somerville, MA), 2004. MR 2497978

[61]L. Erdős, M. Salm­hofer, and H.-T. Yau: “On the quantum Boltzmann equa­tion,” J. Stat­ist. Phys. 116 : 1–​4 (2004), pp. 367–​380. MR 2083147

[62]C. Land­im, J. Quastel, M. Salm­hofer, and H.-T. Yau: “Su­per­dif­fus­iv­ity of asym­met­ric ex­clu­sion pro­cess in di­men­sions one and two,” Comm. Math. Phys. 244 : 3 (2004), pp. 455–​481. MR 2034485 Zbl 1064.​60164

[63]A. El­gart, L. Erdős, B. Schlein, and H.-T. Yau: “Non­lin­ear Hartree equa­tion as the mean field lim­it of weakly coupled fer­mi­ons,” J. Math. Pures Ap­pl. (9) 83 : 10 (2004), pp. 1241–​1273. MR 2092307

[64]C. Land­im, J. A. Ramírez, and H.-T. Yau: “Su­per­dif­fus­iv­ity of two di­men­sion­al lat­tice gas mod­els,” J. Stat. Phys. 119 : 5–​6 (2005), pp. 963–​995. MR 2157854 Zbl 1088.​82016

[65]L. Erdős, M. Salm­hofer, and H.-T. Yau: “To­wards the quantum Browni­an mo­tion,” pp. 233–​257 in Math­em­at­ic­al phys­ics of quantum mech­an­ics. Lec­ture Notes in Phys. 690. Spring­er (Ber­lin), 2006. MR 2234914

[66]A. El­gart, L. Erdős, B. Schlein, and H.-T. Yau: “Gross–Pit­aevskii equa­tion as the mean field lim­it of weakly coupled bo­sons,” Arch. Ra­tion. Mech. Anal. 179 : 2 (2006), pp. 265–​283. MR 2209131

[67]L. Erdős, B. Schlein, and H.-T. Yau: “De­riv­a­tion of the Gross–Pit­aevskii hier­archy for the dy­nam­ics of Bose–Ein­stein con­dens­ate,” Comm. Pure Ap­pl. Math. 59 : 12 (2006), pp. 1659–​1741. MR 2257859

[68]L. Erdős, M. Salm­hofer, and H.-T. Yau: “Quantum dif­fu­sion for the An­der­son mod­el in the scal­ing lim­it,” Ann. Henri Poin­caré 8 : 4 (2007), pp. 621–​685. MR 2333778

[69]L. Erdős, M. Salm­hofer, and H.-T. Yau: “Quantum dif­fu­sion of the ran­dom Schrödinger evol­u­tion in the scal­ing lim­it. II: The re­col­li­sion dia­grams,” Comm. Math. Phys. 271 : 1 (2007), pp. 1–​53. MR 2283953

[70]C.-C. Chen, R. M. Strain, H.-T. Yau, and T.-P. Tsai: “Lower bound on the blow-up rate of the axisym­met­ric Navi­er–Stokes equa­tions,” Int. Math. Res. Not. 2008 : 9 (2008), pp. Art. ID rnn016, 31. MR 2429247

[71]L. Erdős, M. Salm­hofer, and H.-T. Yau: “Feyn­man graphs and renor­mal­iz­a­tion in quantum dif­fu­sion,” pp. 167–​182 in Quantum field the­ory and bey­ond. World Sci. Publ. (Hack­en­sack, NJ), 2008. MR 2588582

[72]L. Erdős, M. Salm­hofer, and H.-T. Yau: “Quantum dif­fu­sion of the ran­dom Schrödinger evol­u­tion in the scal­ing lim­it,” Acta Math. 200 : 2 (2008), pp. 211–​277. MR 2413135

[73]L. Erdős, B. Schlein, and H.-T. Yau: “Rig­or­ous de­riv­a­tion of the Gross–Pit­aevskii equa­tion with a large in­ter­ac­tion po­ten­tial,” J. Amer. Math. Soc. 22 : 4 (2009), pp. 1099–​1156. MR 2525781

[74]C.-C. Chen, R. M. Strain, T.-P. Tsai, and H.-T. Yau: “Lower bounds on the blow-up rate of the axisym­met­ric Navi­er–Stokes equa­tions. II,” Comm. Par­tial Dif­fer­en­tial Equa­tions 34 : 1–​3 (2009), pp. 203–​232. MR 2512859 Zbl 1173.​35095

[75]H.-T. Yau and J. Yin: “The second or­der up­per bound for the ground en­ergy of a Bose gas,” J. Stat. Phys. 136 : 3 (2009), pp. 453–​503. MR 2529681 Zbl 1200.​82002

[76]L. Erdős, B. Schlein, and H.-T. Yau: “Loc­al semi­circle law and com­plete de­lo­c­al­iz­a­tion for Wign­er ran­dom matrices,” Comm. Math. Phys. 287 : 2 (2009), pp. 641–​655. MR 2481753

[77]L. Erdős, B. Schlein, and H.-T. Yau: “Semi­circle law on short scales and de­lo­c­al­iz­a­tion of ei­gen­vectors for Wign­er ran­dom matrices,” Ann. Probab. 37 : 3 (2009), pp. 815–​852. MR 2537522

[78]L. Erdős, J. Ramírez, B. Schlein, T. Tao, V. Vu, and H.-T. Yau: “Bulk uni­ver­sal­ity for Wign­er Her­mitian matrices with subex­po­nen­tial de­cay,” Math. Res. Lett. 17 : 4 (2010), pp. 667–​674. MR 2661171

[79]L. Erdős, S. Péché, J. A. Ramírez, B. Schlein, and H.-T. Yau: “Bulk uni­ver­sal­ity for Wign­er matrices,” Comm. Pure Ap­pl. Math. 63 : 7 (2010), pp. 895–​925. MR 2662426 Zbl 1216.​15025

[80]L. Erdős, B. Schlein, and H.-T. Yau: “De­riv­a­tion of the Gross–Pit­aevskii equa­tion for the dy­nam­ics of Bose-Ein­stein con­dens­ate,” Ann. of Math. (2) 172 : 1 (2010), pp. 291–​370. MR 2680421

[81]H.-T. Yau: “The work of Cédric Vil­lani,” pp. 87–​98 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians, vol. I. Hindus­tan Book Agency (New Del­hi), 2010. MR 2827884 Zbl 05971053

[82]L. Erdős, B. Schlein, and H.-T. Yau: “Wegn­er es­tim­ate and level re­pul­sion for Wign­er ran­dom matrices,” Int. Math. Res. Not. 2010 : 3 (2010), pp. 436–​479. MR 2587574

[83]L. Erdős, J. A. Ramírez, B. Schlein, and H.-T. Yau: “Uni­ver­sal­ity of sine-ker­nel for Wign­er matrices with a small Gaus­si­an per­turb­a­tion,” Elec­tron. J. Probab. 15 (2010), pp. no. 18, 526–​603. MR 2639734

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