-
Previous Article
Equicontinuous sweeping processes
- DCDS-B Home
- This Issue
- Next Article
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.
doi: 10.1239/aap/1231340167. |
[2] |
R. J. Baxter, Corner transfer matrices,, Physica A, 106 (1981), 18.
doi: 10.1016/0378-4371(81)90203-X. |
[3] |
R. J. Baxter, "Exactly Solved Models in Statistical Mechanics,", Academic Press, (1982). |
[4] |
J. E. Besag, Spatial interaction and statistical analysis of lattice systems (with discussion),, J. Roy. Statist. Soc., 36 (1974), 192.
|
[5] |
L. Bogachev, G. Derfel, S. Molchanov and J. Ockendon, On bounded solutions of the balanced generalized pantograph equation,, in, 145 (2008), 29.
|
[6] |
F. Champagnat, J. Idier and Y. Goussard, Stationary Markov random fields on a finite rectangular lattice,, IEEE Trans. Inform. Theory, 44 (1998), 2901.
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.
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.
|
[9] |
T. M. Cover and J. A. Thomas, "Elements of Information Theory,", 2nd ed., (2006).
|
[10] |
G. A. Derfel, Probabilistic method for a class of functional-differential equations,, Ukr. Math. J., 41 (1989), 1137.
|
[11] |
V. Elser, Solution of the dimer problem on a hexagonal lattice with boundary,, J. Phys. A: Math. Gen., 17 (1984), 1509.
|
[12] |
M. E. Fisher, Statistical mechanics of dimers on a plane lattice,, Phys. Rev., 124 (1961), 1664.
|
[13] |
M. Fisher and H. Temperley, The dimer problem in statistical mechanics - an exact result,, Phil. Mag., 6 (1961), 1061. |
[14] |
U. Frisch, "Turbulence: the Legacy of A. N. Kolmogorov,", Cambridge University Press, (1995). |
[15] |
I. I. Gikhman and A. V. Skorokhod, "The Theory of Stochastic Processes,", Springer, (2004).
|
[16] |
J. K. Goutsias, Mutually compatible Gibbs random fields,, IEEE Trans. Inform. Theory, 35 (1989), 1233.
|
[17] |
R. M. Gray, "Entropy and Information Theory,", Springer-Verlag, (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.
|
[19] |
R. A. Horn and C. R. Johnson, "Matrix Analysis,", Cambridge University Press, (2007).
|
[20] |
J. M. Hammersley and V. V. Menon, A lower bound for the monomer-dimer problem,, IMA J. Appl. Maths., 6 (1970), 341.
|
[21] | |
[22] |
J. Idier and Y. Goussard, "Champs de Pickard tridimensionnels,", Tech. Rep., (1999). |
[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. |
[24] |
S. Janson, "Gaussian Hilbert Spaces,'', Cambridge University Press, (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.
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.
|
[27] |
C. Kenyon, D. Randall and A. Sinclair, Approximating the number of monomer-dimer coverings of a lattice,, J. Stat. Phys., 83 (1996), 637.
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., 30 (1997), 767.
|
[29] |
E. H. Lieb, Solution of the dimer problem by the transfer matrix method,, J. Math. Phys., 8 (1967), 2339. |
[30] |
M. Loebl, On the dimer problem and the Ising problem in finite 3-dimensional lattices,, Electr. J. Combinator., 9 (2002), 1.
|
[31] |
K. Mahler, On a special functional equation,, J. London Math. Soc., 15 (1940), 115.
doi: 10.1112/jlms/s1-15.2.115. |
[32] |
P. Malliavin, "Integration and Probability,", Springer-Verlag, (1995).
doi: 10.1007/978-1-4612-4202-4. |
[33] | |
[34] |
N. F. G. Martin and J. W. England, "Mathematical Theory of Entropy,", Addison-Wesley, (1981).
|
[35] |
P.-A. Meyer, "Quantum Probability for Probabilists,", 2nd ed., (1995).
|
[36] |
U. U. Müller, A. Schick and W. Wefelmeyer, Inference for alternating time series,, in:, (2007), 589. |
[37] |
D. K. Pickard, A curious binary lattice process,, J. Appl. Prob., 14 (1977), 717.
doi: 10.2307/3213345. |
[38] |
D. K. Pickard, Unilateral Markov fields,, Adv. Appl. Prob., 12 (1980), 655.
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.
doi: 10.1098/rspa.2000.0621. |
[40] |
H. Rue and L. Held, "Gaussian Markov Random Fields,", Chapman & Hall, (2006). |
[41] | |
[42] |
J. J. Sakurai, "Modern Quantum Mechanics,", Addison-Wesley, (1994). |
[43] |
A. N. Shiryaev, "Probability,", 2nd ed., (1995). |
[44] |
V. Spiridonov, Universal superpositions of coherent states and self-similar potentials,, Phys. Rev. A, 52 (1995), 1909.
doi: 10.1103/PhysRevA.52.1909. |
[45] |
E. M. Tory and D. K. Pickard, Unilateral Gaussian fields,, Adv. Appl. Prob., 24 (1992), 95.
doi: 10.2307/1427731. |
[46] |
I. Vladimirov, "Quantized Linear Systems on Integer Lattices: Frequency-Based Approach,", Center for Applied Dynamical Systems and Environmental Modeling, (1996), 96. |
[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.
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.
doi: 10.1239/aap/1231340167. |
[2] |
R. J. Baxter, Corner transfer matrices,, Physica A, 106 (1981), 18.
doi: 10.1016/0378-4371(81)90203-X. |
[3] |
R. J. Baxter, "Exactly Solved Models in Statistical Mechanics,", Academic Press, (1982). |
[4] |
J. E. Besag, Spatial interaction and statistical analysis of lattice systems (with discussion),, J. Roy. Statist. Soc., 36 (1974), 192.
|
[5] |
L. Bogachev, G. Derfel, S. Molchanov and J. Ockendon, On bounded solutions of the balanced generalized pantograph equation,, in, 145 (2008), 29.
|
[6] |
F. Champagnat, J. Idier and Y. Goussard, Stationary Markov random fields on a finite rectangular lattice,, IEEE Trans. Inform. Theory, 44 (1998), 2901.
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.
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.
|
[9] |
T. M. Cover and J. A. Thomas, "Elements of Information Theory,", 2nd ed., (2006).
|
[10] |
G. A. Derfel, Probabilistic method for a class of functional-differential equations,, Ukr. Math. J., 41 (1989), 1137.
|
[11] |
V. Elser, Solution of the dimer problem on a hexagonal lattice with boundary,, J. Phys. A: Math. Gen., 17 (1984), 1509.
|
[12] |
M. E. Fisher, Statistical mechanics of dimers on a plane lattice,, Phys. Rev., 124 (1961), 1664.
|
[13] |
M. Fisher and H. Temperley, The dimer problem in statistical mechanics - an exact result,, Phil. Mag., 6 (1961), 1061. |
[14] |
U. Frisch, "Turbulence: the Legacy of A. N. Kolmogorov,", Cambridge University Press, (1995). |
[15] |
I. I. Gikhman and A. V. Skorokhod, "The Theory of Stochastic Processes,", Springer, (2004).
|
[16] |
J. K. Goutsias, Mutually compatible Gibbs random fields,, IEEE Trans. Inform. Theory, 35 (1989), 1233.
|
[17] |
R. M. Gray, "Entropy and Information Theory,", Springer-Verlag, (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.
|
[19] |
R. A. Horn and C. R. Johnson, "Matrix Analysis,", Cambridge University Press, (2007).
|
[20] |
J. M. Hammersley and V. V. Menon, A lower bound for the monomer-dimer problem,, IMA J. Appl. Maths., 6 (1970), 341.
|
[21] | |
[22] |
J. Idier and Y. Goussard, "Champs de Pickard tridimensionnels,", Tech. Rep., (1999). |
[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. |
[24] |
S. Janson, "Gaussian Hilbert Spaces,'', Cambridge University Press, (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.
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.
|
[27] |
C. Kenyon, D. Randall and A. Sinclair, Approximating the number of monomer-dimer coverings of a lattice,, J. Stat. Phys., 83 (1996), 637.
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., 30 (1997), 767.
|
[29] |
E. H. Lieb, Solution of the dimer problem by the transfer matrix method,, J. Math. Phys., 8 (1967), 2339. |
[30] |
M. Loebl, On the dimer problem and the Ising problem in finite 3-dimensional lattices,, Electr. J. Combinator., 9 (2002), 1.
|
[31] |
K. Mahler, On a special functional equation,, J. London Math. Soc., 15 (1940), 115.
doi: 10.1112/jlms/s1-15.2.115. |
[32] |
P. Malliavin, "Integration and Probability,", Springer-Verlag, (1995).
doi: 10.1007/978-1-4612-4202-4. |
[33] | |
[34] |
N. F. G. Martin and J. W. England, "Mathematical Theory of Entropy,", Addison-Wesley, (1981).
|
[35] |
P.-A. Meyer, "Quantum Probability for Probabilists,", 2nd ed., (1995).
|
[36] |
U. U. Müller, A. Schick and W. Wefelmeyer, Inference for alternating time series,, in:, (2007), 589. |
[37] |
D. K. Pickard, A curious binary lattice process,, J. Appl. Prob., 14 (1977), 717.
doi: 10.2307/3213345. |
[38] |
D. K. Pickard, Unilateral Markov fields,, Adv. Appl. Prob., 12 (1980), 655.
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.
doi: 10.1098/rspa.2000.0621. |
[40] |
H. Rue and L. Held, "Gaussian Markov Random Fields,", Chapman & Hall, (2006). |
[41] | |
[42] |
J. J. Sakurai, "Modern Quantum Mechanics,", Addison-Wesley, (1994). |
[43] |
A. N. Shiryaev, "Probability,", 2nd ed., (1995). |
[44] |
V. Spiridonov, Universal superpositions of coherent states and self-similar potentials,, Phys. Rev. A, 52 (1995), 1909.
doi: 10.1103/PhysRevA.52.1909. |
[45] |
E. M. Tory and D. K. Pickard, Unilateral Gaussian fields,, Adv. Appl. Prob., 24 (1992), 95.
doi: 10.2307/1427731. |
[46] |
I. Vladimirov, "Quantized Linear Systems on Integer Lattices: Frequency-Based Approach,", Center for Applied Dynamical Systems and Environmental Modeling, (1996), 96. |
[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.
doi: 10.1016/S0378-4754(00)00154-3. |
[1] |
Johnathan M. Bardsley. Gaussian Markov random field priors for inverse problems. Inverse Problems & Imaging, 2013, 7 (2) : 397-416. doi: 10.3934/ipi.2013.7.397 |
[2] |
Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42. |
[3] |
Y. Kabeya. Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition. Discrete & Continuous Dynamical Systems - A, 2006, 14 (1) : 117-134. doi: 10.3934/dcds.2006.14.117 |
[4] |
Zhaojuan Wang, Shengfan Zhou. Random attractor for stochastic non-autonomous damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 545-573. doi: 10.3934/dcds.2017022 |
[5] |
Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund. On Lyapunov exponents of difference equations with random delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 861-874. doi: 10.3934/dcdsb.2015.20.861 |
[6] |
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102 |
[7] |
Yong-Jung Kim. A generalization of the moment problem to a complex measure space and an approximation technique using backward moments. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 187-207. doi: 10.3934/dcds.2011.30.187 |
[8] |
Maria Schonbek, Tomas Schonbek. Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1277-1304. doi: 10.3934/dcds.2005.13.1277 |
[9] |
Wolfgang Wagner. A random cloud model for the Wigner equation. Kinetic & Related Models, 2016, 9 (1) : 217-235. doi: 10.3934/krm.2016.9.217 |
[10] |
Doan Thai Son. On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3113-3126. doi: 10.3934/dcdsb.2017166 |
[11] |
Haiyang Wang, Zhen Wu. Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation. Mathematical Control & Related Fields, 2015, 5 (3) : 651-678. doi: 10.3934/mcrf.2015.5.651 |
[12] |
Fabio Camilli, Elisabetta Carlini, Claudio Marchi. A model problem for Mean Field Games on networks. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4173-4192. doi: 10.3934/dcds.2015.35.4173 |
[13] |
Edward Belbruno. Random walk in the three-body problem and applications. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 519-540. doi: 10.3934/dcdss.2008.1.519 |
[14] |
Tzong-Yow Lee and Fred Torcaso. Wave propagation in a lattice KPP equation in random media. Electronic Research Announcements, 1997, 3: 121-125. |
[15] |
Wolfgang Wagner. A random cloud model for the Schrödinger equation. Kinetic & Related Models, 2014, 7 (2) : 361-379. doi: 10.3934/krm.2014.7.361 |
[16] |
Dan Stanescu, Benito Chen-Charpentier. Random coefficient differential equation models for Monod kinetics. Conference Publications, 2009, 2009 (Special) : 719-728. doi: 10.3934/proc.2009.2009.719 |
[17] |
Wafa Hamrouni, Ali Abdennadher. Random walk's models for fractional diffusion equation. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2509-2530. doi: 10.3934/dcdsb.2016058 |
[18] |
Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control & Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 |
[19] |
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 |
[20] |
Juan Li, Wenqiang Li. Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control & Related Fields, 2015, 5 (3) : 501-516. doi: 10.3934/mcrf.2015.5.501 |
2016 Impact Factor: 0.994
Tools
Metrics
Other articles
by authors
[Back to Top]