메뉴 건너뛰기




Volumn 62, Issue 12, 2009, Pages 1595-1631

The lee-yang and Pólya-Schur programs. II. Theory of stable polynomials and applications

Author keywords

[No Author keywords available]

Indexed keywords


EID: 76749115349     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20295     Document Type: Article
Times cited : (87)

References (62)
  • 1
    • 76749117577 scopus 로고    scopus 로고
    • Sums of entire functions having only real zeros
    • (electronic)
    • Adams, S. R.; Cardon, D. A. Sums of entire functions having only real zeros. Proc. Amer. Math. Soc. 135 (2007), no. 12, 3857-3866 (electronic).
    • (2007) Proc. Amer. Math. Soc. , vol.135 , Issue.12 , pp. 3857-3866
    • Adams, S.R.1    Cardon, D.A.2
  • 2
    • 0009031064 scopus 로고
    • Theorems on the partition functions of the Heisenberg ferromagnets
    • Asano, T. Theorems on the partition functions of the Heisenberg ferromagnets. J. Phys. Soc. Japan 29 (1970), 350-359.
    • (1970) J. Phys. Soc. Japan , vol.29 , pp. 350-359
    • Asano, T.1
  • 3
    • 7544239173 scopus 로고    scopus 로고
    • Partition function zeros at first-order phase transitions: a general analysis
    • Biskup, M.; Borgs, C.; Chayes, J. T.; Kleinwaks, L. J.; Kotecky, R. Partition function zeros at first-order phase transitions: a general analysis. Comm. Math. Phys. 251 (2004), no. 1, 79-131.
    • (2004) Comm. Math. Phys. , vol.251 , Issue.1 , pp. 79-131
    • Biskup, M.1    Borgs, C.2    Chayes, J.T.3    Kleinwaks, L.J.4    Kotecky, R.5
  • 4
    • 4344590030 scopus 로고    scopus 로고
    • Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
    • Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. Partition function zeros at first-order phase transitions: Pirogov-Sinai theory. J. Statist. Phys. 116 (2004), no. 1-4, 97-155.
    • (2004) J. Statist. Phys. , vol.116 , Issue.1-4 , pp. 97-155
    • Biskup, M.1    Borgs, C.2    Chayes, J.T.3    Kotecký, R.4
  • 6
    • 45849094080 scopus 로고    scopus 로고
    • Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products
    • Borcea, J.; Brändén, P. Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products. Duke Math. J. 143 (2008), no. 2, 205-223.
    • (2008) Duke Math. J. , vol.143 , Issue.2 , pp. 205-223
    • Borcea, J.1    Brändén, P.2
  • 7
    • 71449101577 scopus 로고    scopus 로고
    • Pólya-Schur master theorems for circular domains and their boundaries
    • Borcea, J.; Brändén, P. Pólya-Schur master theorems for circular domains and their boundaries. Ann. of Math. (2) 170 (2009), 465-492.
    • (2009) Ann. of Math. (2) , vol.170 , pp. 465-492
    • Borcea, J.1    Brändén, P.2
  • 10
    • 70350670994 scopus 로고    scopus 로고
    • Negative dependence and the geometry of polynomials
    • Borcea, J.; Brändén, P.; Liggett, T. M. Negative dependence and the geometry of polynomials. J. Amer. Math. Soc., 22 (2009), no. 2, 521-567.
    • (2009) J. Amer. Math. Soc. , vol.22 , Issue.2 , pp. 521-567
    • Borcea, J.1    Brändén, P.2    Liggett, T.M.3
  • 11
    • 34548157530 scopus 로고    scopus 로고
    • Polynomials with the half-plane property and matroid theory
    • Brändén, P. Polynomials with the half-plane property and matroid theory. Adv. Math. 216 (2007), no. 1, 302-320.
    • (2007) Adv. Math. , vol.216 , Issue.1 , pp. 302-320
    • Brändén, P.1
  • 12
    • 0042104489 scopus 로고
    • An analogue of Grace's apolarity theorem
    • Bruijn, N. G. de. An analogue of Grace's apolarity theorem. Nieuw Arch. Wiskunde (2) 23 (1949), 69-76.
    • (1949) Nieuw Arch. Wiskunde (2) , vol.23 , pp. 69-76
    • de Bruijn, N.G.1
  • 13
    • 0011625408 scopus 로고
    • Some theorems on the roots of polynomials
    • Bruijn, N. G. de. Some theorems on the roots of polynomials. Nieuw Arch. Wiskunde (2) 23 (1949), 66-68.
    • (1949) Nieuw Arch. Wiskunde (2) , vol.23 , pp. 66-68
    • de Bruijn, N.G.1
  • 14
    • 1842591159 scopus 로고    scopus 로고
    • Sums of exponential functions having only real zeros
    • Cardon, D. A. Sums of exponential functions having only real zeros. Manuscripta Math. 113 (2004), no. 3, 307-317.
    • (2004) Manuscripta Math , vol.113 , Issue.3 , pp. 307-317
    • Cardon, D.A.1
  • 15
    • 18144401681 scopus 로고    scopus 로고
    • Fourier transforms having only real zeros
    • (electronic)
    • Cardon, D. A. Fourier transforms having only real zeros. Proc. Amer. Math. Soc. 133 (2005), no. 5, 1349-1356 (electronic).
    • (2005) Proc. Amer. Math. Soc. , vol.133 , Issue.5 , pp. 1349-1356
    • Cardon, D.A.1
  • 16
    • 0346401580 scopus 로고    scopus 로고
    • Homogeneous multivariate polynomials with the half-plane property
    • Choe, Y.-B.; Oxley, J. G.; Sokal, A. D.; Wagner, D. G. Homogeneous multivariate polynomials with the half-plane property. Adv. in Appl. Math. 32 (2004), no. 1-2, 88-187.
    • (2004) Adv. in Appl. Math. , vol.32 , Issue.1-2 , pp. 88-187
    • Choe, Y.-B.1    Oxley, J.G.2    Sokal, A.D.3    Wagner, D.G.4
  • 17
    • 84972545881 scopus 로고
    • Multiplier sequences for fields
    • Craven, T.; Csordas, G. Multiplier sequences for fields. Illinois J. Math. 21 (1977), no. 4, 801-817.
    • (1977) Illinois J. Math. , vol.21 , Issue.4 , pp. 801-817
    • Craven, T.1    Csordas, G.2
  • 18
    • 28844496199 scopus 로고    scopus 로고
    • Composition theorems, multiplier sequences and complex zero decreasing sequences
    • Advances in Complex Analysis and Its Applications, 3. Kluwer, Boston
    • Craven, T.; Csordas, G. Composition theorems, multiplier sequences and complex zero decreasing sequences. Value distribution theory and related topics, 131-166. Advances in Complex Analysis and Its Applications, 3. Kluwer, Boston, 2004.
    • (2004) Value distribution theory and related topics , pp. 131-166
    • Craven, T.1    Csordas, G.2
  • 19
    • 0001094667 scopus 로고
    • The zeros of derivatives of entire functions and the Pólya-Wiman conjecture
    • Craven, T.; Csordas, G.; Smith, W. The zeros of derivatives of entire functions and the Pólya-Wiman conjecture. Ann. of Math. (2) 125 (1987), no. 2, 405-431.
    • (1987) Ann. of Math. (2) , vol.125 , Issue.2 , pp. 405-431
    • Craven, T.1    Csordas, G.2    Smith, W.3
  • 20
    • 70350691598 scopus 로고    scopus 로고
    • Linear operators and the distribution of zeros of entire functions
    • Csordas, G. Linear operators and the distribution of zeros of entire functions. Complex Var. Elliptic Equ. 51 (2006), no. 7, 625-632.
    • (2006) Complex Var. Elliptic Equ. , vol.51 , Issue.7 , pp. 625-632
    • Csordas, G.1
  • 23
    • 0000199940 scopus 로고    scopus 로고
    • Theory of monomer-dimer systems
    • Heilmann, O. J.; Lieb, E. H. Theory of monomer-dimer systems. Comm. Math. Phys. 25 (1972), 190-232.
    • Comm. Math. Phys. , vol.25 , Issue.1972 , pp. 190-232
    • Heilmann, O.J.1    Lieb, E.H.2
  • 24
    • 34247216675 scopus 로고    scopus 로고
    • Linear matrix inequality representation of sets
    • Helton, J.; Vinnikov, V. Linear matrix inequality representation of sets. Comm. Pure Appl. Math. 60 (2007), no. 5, 654-674.
    • (2007) Comm. Pure Appl. Math. , vol.60 , Issue.5 , pp. 654-674
    • Helton, J.1    Vinnikov, V.2
  • 25
    • 0346907809 scopus 로고    scopus 로고
    • Schur products of certain polynomials
    • Contemporary Mathematics, 211. American Mathematical Society, Providence, R. I
    • Hinkkanen, A. Schur products of certain polynomials. Lipa's legacy (New York, 1995), 285-295. Contemporary Mathematics, 211. American Mathematical Society, Providence, R.I., 1997.
    • (1997) Lipa's legacy (New York, 1995) , pp. 285-295
    • Hinkkanen, A.1
  • 26
  • 29
    • 0012566413 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents I. Half-plane exponents
    • Lawler, G. F.; Schramm, O.; Werner, W. Values of Brownian intersection exponents. I. Half-plane exponents. Acta Math. 187 (2001), no. 2, 237-273.
    • (2001) Acta Math , vol.187 , Issue.2 , pp. 237-273
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 31
    • 0000704106 scopus 로고
    • Statistical theory of equations of state and phase transitions II. Lattice gas and Ising model
    • Lee, T. D.; Yang, C. N. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Physical Rev. (2) 87 (1952), 410-419.
    • (1952) Physical Rev. (2) , vol.87 , pp. 410-419
    • Lee, T.D.1    Yang, C.N.2
  • 32
    • 0004248071 scopus 로고
    • Distribution of zeros of entire functions
    • Revised ed. Translations of Mathematical Monographs, 5. American Mathematical Society, Providence, R.I.
    • Levin, B. J. Distribution of zeros of entire functions. Revised ed. Translations of Mathematical Monographs, 5. American Mathematical Society, Providence, R.I., 1980.
    • (1980)
    • Levin, B.J.1
  • 33
    • 0000888415 scopus 로고
    • A general Lee-Yang theorem for one-component and multicomponent ferromagnets
    • Lieb, E. H.; Sokal, A. D. A general Lee-Yang theorem for one-component and multicomponent ferromagnets. Comm. Math. Phys. 80 (1981), no. 2, 153-179.
    • (1981) Comm. Math. Phys. , vol.80 , Issue.2 , pp. 153-179
    • Lieb, E.H.1    Sokal, A.D.2
  • 34
    • 0004139016 scopus 로고
    • Grundlehren der Mathematischen Wissenschaften, Springer, New York
    • Liggett, T. M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften, 276. Springer, New York, 1985.
    • (1985) Interacting particle systems , pp. 276
    • Liggett, T.M.1
  • 35
    • 57149086146 scopus 로고    scopus 로고
    • Distributional limits for the symmetric exclusion process
    • Liggett, T. M. Distributional limits for the symmetric exclusion process. Stochastic Process. Appl. 119 (2009), no. 1, 1-15.
    • (2009) Stochastic Process. Appl. , vol.119 , Issue.1 , pp. 1-15
    • Liggett, T.M.1
  • 37
    • 84980134264 scopus 로고
    • Zeros of the partition function for generalized Ising systems
    • Newman, C. M. Zeros of the partition function for generalized Ising systems. Comm. Pure Appl. Math. 27 (1974), 143-159.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 143-159
    • Newman, C.M.1
  • 38
    • 0009080966 scopus 로고
    • Gaussian correlation inequalities for ferromagnets
    • Newman, C. M. Gaussian correlation inequalities for ferromagnets. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 33 (1975/76), no. 2, 75-93.
    • (1975) Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.33 , Issue.2 , pp. 75-93
    • Newman, C.M.1
  • 39
    • 0343344067 scopus 로고
    • Inequalities for Ising models and field theories which obey the Lee-Yang theorem
    • Newman, C. M. Inequalities for Ising models and field theories which obey the Lee-Yang theorem. Comm. Math. Phys. 41 (1975), 1-9.
    • (1975) Comm. Math. Phys. , vol.41 , pp. 1-9
    • Newman, C.M.1
  • 40
    • 51249195756 scopus 로고
    • Bemerkung über die Integraldarstellung der Riemannsche ξ-Funktion
    • Pólya, G. Bemerkung über die Integraldarstellung der Riemannsche ξ-Funktion. Acta Math. 48 (1926), no. 3-4, 305-317.
    • (1926) Acta Math , vol.48 , Issue.3-4 , pp. 305-317
    • Pólya, G.1
  • 41
    • 33746869683 scopus 로고
    • Location of zeros. Mathematicians of Our Time, 8. MIT Press, Cambridge, Mass.-London
    • Pólya, G. Collected papers. Vol. II: Location of zeros. Mathematicians of Our Time, 8. MIT Press, Cambridge, Mass.-London, 1974.
    • (1974) Collected papers , vol.2
    • Pólya, G.1
  • 42
    • 84941393156 scopus 로고
    • Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen
    • Pólya, G.; Schur, I. Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen. J. Reine Angew. Math. 144 (1914), 89-113.
    • (1914) J. Reine Angew. Math. , vol.144 , pp. 89-113
    • Pólya, G.1    Schur, I.2
  • 44
    • 0009333526 scopus 로고    scopus 로고
    • London Mathematical Society Monographs. New Series, 26. Clarendon, Oxford University Press, Oxford
    • Rahman, Q. I.; Schmeisser, G. Analytic theory of polynomials. London Mathematical Society Monographs. New Series, 26. Clarendon, Oxford University Press, Oxford, 2002.
    • (2002) Analytic theory of polynomials
    • Rahman, Q.I.1    Schmeisser, G.2
  • 45
    • 0033473448 scopus 로고    scopus 로고
    • Two turning points in invariant theory
    • Rota, G.-C. Two turning points in invariant theory. Math. Intelligencer 21 (1999), 20-27.
    • (1999) Math. Intelligencer , vol.21 , pp. 20-27
    • Rota, G.-C.1
  • 46
    • 0001578337 scopus 로고
    • Extension of the Lee-Yang circle theorem
    • Ruelle, D. Extension of the Lee-Yang circle theorem. Phys. Rev. Lett. 26 (1971), 303-304.
    • (1971) Phys. Rev. Lett. , vol.26 , pp. 303-304
    • Ruelle, D.1
  • 47
    • 0009032710 scopus 로고
    • Some remarks on the location of zeroes of the partition function for lattice systems
    • Ruelle, D. Some remarks on the location of zeroes of the partition function for lattice systems. Comm. Math. Phys. 31 (1973), 265-277.
    • (1973) Comm. Math. Phys. , vol.31 , pp. 265-277
    • Ruelle, D.1
  • 48
    • 84968505456 scopus 로고
    • Is our mathematics natural? The case of equilibrium statistical mechanics
    • Ruelle, D. Is our mathematics natural? The case of equilibrium statistical mechanics. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 1, 259-268.
    • (1988) Bull. Amer. Math. Soc. (N.S.) , vol.19 , Issue.1 , pp. 259-268
    • Ruelle, D.1
  • 49
    • 0347760568 scopus 로고    scopus 로고
    • Counting unbranched subgraphs
    • Ruelle, D. Counting unbranched subgraphs. J. Algebraic Combin. 9 (1999), no. 2, 157-160.
    • (1999) J. Algebraic Combin. , vol.9 , Issue.2 , pp. 157-160
    • Ruelle, D.1
  • 51
    • 0033248103 scopus 로고    scopus 로고
    • Zeros of graph-counting polynomials
    • Ruelle, D. Zeros of graph-counting polynomials. Comm. Math. Phys. 200 (1999), no. 1, 43-56.
    • (1999) Comm. Math. Phys. , vol.200 , Issue.1 , pp. 43-56
    • Ruelle, D.1
  • 53
    • 0011562716 scopus 로고
    • Zwei Sätze über algebraische Gleichungen mit lauter reellen Wurzeln
    • Schur, I. Zwei Sätze über algebraische Gleichungen mit lauter reellen Wurzeln. J. Reine Angew. Math. 144 (1923), 75-88.
    • (1923) J. Reine Angew. Math. , vol.144 , pp. 75-88
    • Schur, I.1
  • 54
    • 17544380550 scopus 로고    scopus 로고
    • The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma
    • Scott, A. D.; Sokal, A. D. The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma. J. Stat. Phys. 118 (2005), no. 5-6, 1151-1261.
    • (2005) J. Stat. Phys. , vol.118 , Issue.5-6 , pp. 1151-1261
    • Scott, A.D.1    Sokal, A.D.2
  • 55
    • 34249976818 scopus 로고
    • Apolarity its applications
    • Shepherd-Barron, N. I. Apolarity and its applications. Invent. Math. 97 (1989), no. 2, 433-444.
    • (1989) Invent. Math. , vol.97 , Issue.2 , pp. 433-444
    • Shepherd-Barron, N.I.1
  • 56
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • Smirnov, S.; Werner, W. Critical exponents for two-dimensional percolation. Math. Res. Lett. 8 (2001), no. 5-6, 729-744.
    • (2001) Math. Res. Lett. , vol.8 , Issue.5-6 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 57
    • 29844450023 scopus 로고    scopus 로고
    • The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
    • London Mathematical Society Lecture Note Series, 327. Cambridge University Press, Cambridge
    • Sokal, A. D. The multivariate Tutte polynomial (alias Potts model) for graphs and matroids. Surveys in combinatorics 2005, 173-226. London Mathematical Society Lecture Note Series, 327. Cambridge University Press, Cambridge, 2005.
    • (2005) Surveys in combinatorics 2005 , pp. 173-226
    • Sokal, A.D.1
  • 59
    • 0008989355 scopus 로고    scopus 로고
    • Multipartition series
    • Wagner, D. G. Multipartition series. SIAM J. Discrete Math. 9 (1996), no. 4, 529-544.
    • (1996) SIAM J. Discrete Math. , vol.9 , Issue.4 , pp. 529-544
    • Wagner, D.G.1
  • 60
    • 56449127151 scopus 로고    scopus 로고
    • Weighted enumeration of spanning subgraphs with degree constraints
    • Wagner, D. G. Weighted enumeration of spanning subgraphs with degree constraints. J. Combin. Theory Ser. B. 99 (2009), no. 2, 347-357.
    • (2009) J. Combin. Theory Ser. B. , vol.99 , Issue.2 , pp. 347-357
    • Wagner, D.G.1
  • 61
    • 0011278880 scopus 로고
    • On the location of the roots of certain types of polynomials
    • Walsh, J. L. On the location of the roots of certain types of polynomials. Trans. Amer. Math. Soc. 24 (1922), no. 3, 163-180.
    • (1922) Trans. Amer. Math. Soc. , vol.24 , Issue.3 , pp. 163-180
    • Walsh, J.L.1
  • 62
    • 36149023450 scopus 로고
    • Statistical theory of equations of state and phase transitions I. Theory of condensation
    • Yang, C. N.; Lee, T. D. Statistical theory of equations of state and phase transitions. I. Theory of condensation. Physical Rev. (2) 87 (1952), 404-409.
    • (1952) Physical Rev. (2) , vol.87 , pp. 404-409
    • Yang, C.N.1    Lee, T.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.