- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
Equicontinuous sweeping processes
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
1. | University of New South Wales, Canberra, ACT 2600, Australia |
References:
[1] |
V. V. Anh, N .N. Leonenko and N. R. Shieh, Multifractality of products of geometric Ornstein-Uhlenbeck type processes, Adv. Appl. Prob., 40 (2008), 1129-1156.
doi: 10.1239/aap/1231340167. |
[2] |
R. J. Baxter, Corner transfer matrices, Physica A, 106 (1981), 18-27.
doi: 10.1016/0378-4371(81)90203-X. |
[3] |
R. J. Baxter, "Exactly Solved Models in Statistical Mechanics," Academic Press, London, 1982. |
[4] |
J. E. Besag, Spatial interaction and statistical analysis of lattice systems (with discussion), J. Roy. Statist. Soc., Series B, 36 (1974), 192-236. |
[5] |
L. Bogachev, G. Derfel, S. Molchanov and J. Ockendon, On bounded solutions of the balanced generalized pantograph equation, in "Topics in Stochastic Analysis and Nonparametric Estimation" IMA Vol. Math. Appl., 145 29-49, Springer, New York, 2008. |
[6] |
F. Champagnat, J. Idier and Y. Goussard, Stationary Markov random fields on a finite rectangular lattice, IEEE Trans. Inform. Theory, 44 (1998), 2901-2916.
doi: 10.1109/18.737521. |
[7] |
F. Champagnat and J. Idier, On the correlation structure of unilateral AR processes on the plane, Adv. Appl. Prob., 32 (2000), 408-425.
doi: 10.1239/aap/1013540171. |
[8] |
N. Cressie and J. L. Davidson, Image analysis with partially ordered Markov models, Comput. Stat. Data Anal., 29 (1998), 1-26. |
[9] |
T. M. Cover and J. A. Thomas, "Elements of Information Theory," 2nd ed., Wiley, Hoboken, New Jersey, 2006. |
[10] |
G. A. Derfel, Probabilistic method for a class of functional-differential equations, Ukr. Math. J., 41 (1989), 1137-1141. |
[11] |
V. Elser, Solution of the dimer problem on a hexagonal lattice with boundary, J. Phys. A: Math. Gen., 17 (1984), 1509-1513. |
[12] |
M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev., 124 (1961), 1664-1672. |
[13] |
M. Fisher and H. Temperley, The dimer problem in statistical mechanics - an exact result, Phil. Mag., 6 (1961), 1061-1063. |
[14] |
U. Frisch, "Turbulence: the Legacy of A. N. Kolmogorov," Cambridge University Press, Cambridge, 1995. |
[15] |
I. I. Gikhman and A. V. Skorokhod, "The Theory of Stochastic Processes," Springer, Berlin, 2004. |
[16] |
J. K. Goutsias, Mutually compatible Gibbs random fields, IEEE Trans. Inform. Theory, 35 (1989), 1233-1249. |
[17] |
R. M. Gray, "Entropy and Information Theory," Springer-Verlag, New York, 1990. |
[18] |
R. Hayn and V. N. Plechko, Grassmann variable analysis for dimer problems in two dimensions, J. Phys. A: Math. Gen., 27 (1994), 4753-4760. |
[19] |
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, New York, 2007. |
[20] |
J. M. Hammersley and V. V. Menon, A lower bound for the monomer-dimer problem, IMA J. Appl. Maths., 6 (1970), 341-364. |
[21] |
K. Huang, "Statistical Mechanics," 2nd ed., John Wiley & Sons, New York, 1987. |
[22] |
J. Idier and Y. Goussard, "Champs de Pickard tridimensionnels," Tech. Rep., IGB/GPI-LSS, 1999, http://www.irccyn.ec-nantes.fr/~idier/pub/idier99d.pdf. |
[23] |
L. Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika, 12 (1918), 134-139. |
[24] |
S. Janson, "Gaussian Hilbert Spaces,'' Cambridge University Press, Cambridge, 1997. |
[25] |
P. W. Kasteleyn, The statistics of dimers on a lattice I. The number of dimer arrangements on a quadratic lattice, Physica, 27 (1961), 1209-1225.
doi: 10.1016/0031-8914(61)90063-5. |
[26] |
T. Kato and J. B. McLeod, The functional-differential equation $y'(x) = ay(\lambda x) + by(x)$, Bull. Amer. Math. Soc., 77 (1971), 891-937. |
[27] |
C. Kenyon, D. Randall and A. Sinclair, Approximating the number of monomer-dimer coverings of a lattice, J. Stat. Phys., 83 (1996), 637-659.
doi: 10.1007/BF02183743. |
[28] |
V. Kozyakin, N. Kuznetsov, A. Pokrovskii and I. Vladimirov, Some problems in analysis of discretizations of continuous dynamical systems, Nonlin. Anal., Theor. Meth. Appl., 30 (1997), 767-778. |
[29] |
E. H. Lieb, Solution of the dimer problem by the transfer matrix method, J. Math. Phys., 8 (1967), 2339-2341. |
[30] |
M. Loebl, On the dimer problem and the Ising problem in finite 3-dimensional lattices, Electr. J. Combinator., 9 (2002), 1-25. |
[31] |
K. Mahler, On a special functional equation, J. London Math. Soc., 15 (1940), 115-123.
doi: 10.1112/jlms/s1-15.2.115. |
[32] |
P. Malliavin, "Integration and Probability," Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4202-4. |
[33] |
P. Malliavin, "Stochastic Analysis," Springer, Berlin, 1997. |
[34] |
N. F. G. Martin and J. W. England, "Mathematical Theory of Entropy," Addison-Wesley, Reading, Mass., 1981. |
[35] |
P.-A. Meyer, "Quantum Probability for Probabilists," 2nd ed., Springer, Berlin, 1995. |
[36] |
U. U. Müller, A. Schick and W. Wefelmeyer, Inference for alternating time series, in: "Recent Advances in Stochastic Modeling and Data Analysis'' (ed. C. H. Skiadas), World Scientific, Singapore, (2007), 589-596. |
[37] |
D. K. Pickard, A curious binary lattice process, J. Appl. Prob., 14 (1977), 717-731.
doi: 10.2307/3213345. |
[38] |
D. K. Pickard, Unilateral Markov fields, Adv. Appl. Prob., 12 (1980), 655-671.
doi: 10.2307/1426425. |
[39] |
A. V. Pokrovskii, A. J. Kent and J. G. McInerney, Mixed moments of random mappings and chaotic dynamical systems, Proc. R. Soc. Lond. A, 456 (2000), 2465-2487.
doi: 10.1098/rspa.2000.0621. |
[40] |
H. Rue and L. Held, "Gaussian Markov Random Fields," Chapman & Hall, 2006. |
[41] |
D. Ruelle, "Thermodynamic Formalism," 2nd ed., Cambridge University Press, Cambridge, 2004. |
[42] |
J. J. Sakurai, "Modern Quantum Mechanics," Addison-Wesley, Reading, Mass., 1994. |
[43] |
A. N. Shiryaev, "Probability," 2nd ed., Springer, New York, 1995. |
[44] |
V. Spiridonov, Universal superpositions of coherent states and self-similar potentials, Phys. Rev. A, 52 (1995), 1909-1935.
doi: 10.1103/PhysRevA.52.1909. |
[45] |
E. M. Tory and D. K. Pickard, Unilateral Gaussian fields, Adv. Appl. Prob., 24 (1992), 95-112.
doi: 10.2307/1427731. |
[46] |
I. Vladimirov, "Quantized Linear Systems on Integer Lattices: Frequency-Based Approach," Center for Applied Dynamical Systems and Environmental Modeling, Deakin University, Geelong, Victoria, Australia, CADSEM Reports 96-032 (1996), 1-37; 96-033 (1996), 1-50. |
[47] |
I. Vladimirov, N. Kuznetsov and P. Diamond, Frequency measurability, algebras of quasiperiodic sets and spatial discretizations of smooth dynamical systems, Math. Comp. Simul., 52 (2000), 251-272.
doi: 10.1016/S0378-4754(00)00154-3. |
show all references
References:
[1] |
V. V. Anh, N .N. Leonenko and N. R. Shieh, Multifractality of products of geometric Ornstein-Uhlenbeck type processes, Adv. Appl. Prob., 40 (2008), 1129-1156.
doi: 10.1239/aap/1231340167. |
[2] |
R. J. Baxter, Corner transfer matrices, Physica A, 106 (1981), 18-27.
doi: 10.1016/0378-4371(81)90203-X. |
[3] |
R. J. Baxter, "Exactly Solved Models in Statistical Mechanics," Academic Press, London, 1982. |
[4] |
J. E. Besag, Spatial interaction and statistical analysis of lattice systems (with discussion), J. Roy. Statist. Soc., Series B, 36 (1974), 192-236. |
[5] |
L. Bogachev, G. Derfel, S. Molchanov and J. Ockendon, On bounded solutions of the balanced generalized pantograph equation, in "Topics in Stochastic Analysis and Nonparametric Estimation" IMA Vol. Math. Appl., 145 29-49, Springer, New York, 2008. |
[6] |
F. Champagnat, J. Idier and Y. Goussard, Stationary Markov random fields on a finite rectangular lattice, IEEE Trans. Inform. Theory, 44 (1998), 2901-2916.
doi: 10.1109/18.737521. |
[7] |
F. Champagnat and J. Idier, On the correlation structure of unilateral AR processes on the plane, Adv. Appl. Prob., 32 (2000), 408-425.
doi: 10.1239/aap/1013540171. |
[8] |
N. Cressie and J. L. Davidson, Image analysis with partially ordered Markov models, Comput. Stat. Data Anal., 29 (1998), 1-26. |
[9] |
T. M. Cover and J. A. Thomas, "Elements of Information Theory," 2nd ed., Wiley, Hoboken, New Jersey, 2006. |
[10] |
G. A. Derfel, Probabilistic method for a class of functional-differential equations, Ukr. Math. J., 41 (1989), 1137-1141. |
[11] |
V. Elser, Solution of the dimer problem on a hexagonal lattice with boundary, J. Phys. A: Math. Gen., 17 (1984), 1509-1513. |
[12] |
M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev., 124 (1961), 1664-1672. |
[13] |
M. Fisher and H. Temperley, The dimer problem in statistical mechanics - an exact result, Phil. Mag., 6 (1961), 1061-1063. |
[14] |
U. Frisch, "Turbulence: the Legacy of A. N. Kolmogorov," Cambridge University Press, Cambridge, 1995. |
[15] |
I. I. Gikhman and A. V. Skorokhod, "The Theory of Stochastic Processes," Springer, Berlin, 2004. |
[16] |
J. K. Goutsias, Mutually compatible Gibbs random fields, IEEE Trans. Inform. Theory, 35 (1989), 1233-1249. |
[17] |
R. M. Gray, "Entropy and Information Theory," Springer-Verlag, New York, 1990. |
[18] |
R. Hayn and V. N. Plechko, Grassmann variable analysis for dimer problems in two dimensions, J. Phys. A: Math. Gen., 27 (1994), 4753-4760. |
[19] |
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, New York, 2007. |
[20] |
J. M. Hammersley and V. V. Menon, A lower bound for the monomer-dimer problem, IMA J. Appl. Maths., 6 (1970), 341-364. |
[21] |
K. Huang, "Statistical Mechanics," 2nd ed., John Wiley & Sons, New York, 1987. |
[22] |
J. Idier and Y. Goussard, "Champs de Pickard tridimensionnels," Tech. Rep., IGB/GPI-LSS, 1999, http://www.irccyn.ec-nantes.fr/~idier/pub/idier99d.pdf. |
[23] |
L. Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika, 12 (1918), 134-139. |
[24] |
S. Janson, "Gaussian Hilbert Spaces,'' Cambridge University Press, Cambridge, 1997. |
[25] |
P. W. Kasteleyn, The statistics of dimers on a lattice I. The number of dimer arrangements on a quadratic lattice, Physica, 27 (1961), 1209-1225.
doi: 10.1016/0031-8914(61)90063-5. |
[26] |
T. Kato and J. B. McLeod, The functional-differential equation $y'(x) = ay(\lambda x) + by(x)$, Bull. Amer. Math. Soc., 77 (1971), 891-937. |
[27] |
C. Kenyon, D. Randall and A. Sinclair, Approximating the number of monomer-dimer coverings of a lattice, J. Stat. Phys., 83 (1996), 637-659.
doi: 10.1007/BF02183743. |
[28] |
V. Kozyakin, N. Kuznetsov, A. Pokrovskii and I. Vladimirov, Some problems in analysis of discretizations of continuous dynamical systems, Nonlin. Anal., Theor. Meth. Appl., 30 (1997), 767-778. |
[29] |
E. H. Lieb, Solution of the dimer problem by the transfer matrix method, J. Math. Phys., 8 (1967), 2339-2341. |
[30] |
M. Loebl, On the dimer problem and the Ising problem in finite 3-dimensional lattices, Electr. J. Combinator., 9 (2002), 1-25. |
[31] |
K. Mahler, On a special functional equation, J. London Math. Soc., 15 (1940), 115-123.
doi: 10.1112/jlms/s1-15.2.115. |
[32] |
P. Malliavin, "Integration and Probability," Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4202-4. |
[33] |
P. Malliavin, "Stochastic Analysis," Springer, Berlin, 1997. |
[34] |
N. F. G. Martin and J. W. England, "Mathematical Theory of Entropy," Addison-Wesley, Reading, Mass., 1981. |
[35] |
P.-A. Meyer, "Quantum Probability for Probabilists," 2nd ed., Springer, Berlin, 1995. |
[36] |
U. U. Müller, A. Schick and W. Wefelmeyer, Inference for alternating time series, in: "Recent Advances in Stochastic Modeling and Data Analysis'' (ed. C. H. Skiadas), World Scientific, Singapore, (2007), 589-596. |
[37] |
D. K. Pickard, A curious binary lattice process, J. Appl. Prob., 14 (1977), 717-731.
doi: 10.2307/3213345. |
[38] |
D. K. Pickard, Unilateral Markov fields, Adv. Appl. Prob., 12 (1980), 655-671.
doi: 10.2307/1426425. |
[39] |
A. V. Pokrovskii, A. J. Kent and J. G. McInerney, Mixed moments of random mappings and chaotic dynamical systems, Proc. R. Soc. Lond. A, 456 (2000), 2465-2487.
doi: 10.1098/rspa.2000.0621. |
[40] |
H. Rue and L. Held, "Gaussian Markov Random Fields," Chapman & Hall, 2006. |
[41] |
D. Ruelle, "Thermodynamic Formalism," 2nd ed., Cambridge University Press, Cambridge, 2004. |
[42] |
J. J. Sakurai, "Modern Quantum Mechanics," Addison-Wesley, Reading, Mass., 1994. |
[43] |
A. N. Shiryaev, "Probability," 2nd ed., Springer, New York, 1995. |
[44] |
V. Spiridonov, Universal superpositions of coherent states and self-similar potentials, Phys. Rev. A, 52 (1995), 1909-1935.
doi: 10.1103/PhysRevA.52.1909. |
[45] |
E. M. Tory and D. K. Pickard, Unilateral Gaussian fields, Adv. Appl. Prob., 24 (1992), 95-112.
doi: 10.2307/1427731. |
[46] |
I. Vladimirov, "Quantized Linear Systems on Integer Lattices: Frequency-Based Approach," Center for Applied Dynamical Systems and Environmental Modeling, Deakin University, Geelong, Victoria, Australia, CADSEM Reports 96-032 (1996), 1-37; 96-033 (1996), 1-50. |
[47] |
I. Vladimirov, N. Kuznetsov and P. Diamond, Frequency measurability, algebras of quasiperiodic sets and spatial discretizations of smooth dynamical systems, Math. Comp. Simul., 52 (2000), 251-272.
doi: 10.1016/S0378-4754(00)00154-3. |
[1] |
Johnathan M. Bardsley. Gaussian Markov random field priors for inverse problems. Inverse Problems and Imaging, 2013, 7 (2) : 397-416. doi: 10.3934/ipi.2013.7.397 |
[2] |
Sheng Zhang, Xiu Yang, Samy Tindel, Guang Lin. Augmented Gaussian random field: Theory and computation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 931-957. doi: 10.3934/dcdss.2021098 |
[3] |
Pedro Duarte, Silvius Klein, Manuel Santos. A random cocycle with non Hölder Lyapunov exponent. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4841-4861. doi: 10.3934/dcds.2019197 |
[4] |
Rajeshwari Majumdar, Phanuel Mariano, Hugo Panzo, Lowen Peng, Anthony Sisti. Lyapunov exponent and variance in the CLT for products of random matrices related to random Fibonacci sequences. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4779-4799. doi: 10.3934/dcdsb.2020126 |
[5] |
Justyna Jarczyk, Witold Jarczyk. Gaussian iterative algorithm and integrated automorphism equation for random means. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6837-6844. doi: 10.3934/dcds.2020135 |
[6] |
Josselin Garnier, Knut Sølna. Enhanced Backscattering of a partially coherent field from an anisotropic random lossy medium. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 1171-1195. doi: 10.3934/dcdsb.2020158 |
[7] |
Fumihiko Nakamura, Yushi Nakano, Hisayoshi Toyokawa. Lyapunov exponents for random maps. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022058 |
[8] |
Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42. |
[9] |
Tian Chen, Zhen Wu. A general maximum principle for partially observed mean-field stochastic system with random jumps in progressive structure. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022012 |
[10] |
Zhaojuan Wang, Shengfan Zhou. Random attractor for stochastic non-autonomous damped wave equation with critical exponent. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 545-573. doi: 10.3934/dcds.2017022 |
[11] |
Y. Kabeya. Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 117-134. doi: 10.3934/dcds.2006.14.117 |
[12] |
Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund. On Lyapunov exponents of difference equations with random delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 861-874. doi: 10.3934/dcdsb.2015.20.861 |
[13] |
Yuxuan Gong, Xiang Xu. Inverse random source problem for biharmonic equation in two dimensions. Inverse Problems and Imaging, 2019, 13 (3) : 635-652. doi: 10.3934/ipi.2019029 |
[14] |
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102 |
[15] |
Yong-Jung Kim. A generalization of the moment problem to a complex measure space and an approximation technique using backward moments. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 187-207. doi: 10.3934/dcds.2011.30.187 |
[16] |
Yuta Tanoue. Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 53-60. doi: 10.3934/puqr.2021003 |
[17] |
Zhenghong Qiu, Jianhui Huang, Tinghan Xie. Linear-Quadratic-Gaussian mean-field controls of social optima. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021047 |
[18] |
Maria Schonbek, Tomas Schonbek. Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1277-1304. doi: 10.3934/dcds.2005.13.1277 |
[19] |
Max-Olivier Hongler. Mean-field games and swarms dynamics in Gaussian and non-Gaussian environments. Journal of Dynamics and Games, 2020, 7 (1) : 1-20. doi: 10.3934/jdg.2020001 |
[20] |
Wolfgang Wagner. A random cloud model for the Wigner equation. Kinetic and Related Models, 2016, 9 (1) : 217-235. doi: 10.3934/krm.2016.9.217 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]