Jacek Miękisz
Evolutionary game theory
Evolutionary game theory and population dynamics
Lecture notes based on the short course given
in the Stefan Banach International Mathematical Center in the framework
of the CIME Summer School ``From a Microscopic to a Macroscopic Description of Complex Systems"
which was held in Będlewo, Poland, 4-9 September 2006.
Abstract, Paper
1. Stochastic stability in spatial games,
J. Stat. Phys. 117: 99-110 (2004).
Abstract, Paper
2. Statistical mechanics of spatial evolutionary games,
J. Phys. A: Math. Gen. 37: 9891-9906 (2004).
Abstract, Paper
3. Stochastic stability in spatial three-player games,
Physica A 343: 175-184 (2004).
Abstract, Paper
4. Stability of evolutionarily stable strategies in discrete replicator dynamics
with time delay (with J. Alboszta), J. Theor. Biol. 231: 175-179 (2004).
Abstract, Paper
5. Evolutionary and asymptotic stability in symmetric multi-player games
(with M. Bukowski), Int. J. Game Theory 33: 41-54 (2004).
Abstract, Paper
6. Long-run behavior of games with many players,
Markov Processes and Related Fields 11: 371-388 (2005).
Abstract, Paper
7. Equilibrium selection in evolutionary games with random matching of players,
J. Theor. Biol. 232: 47-53 (2005).
Abstract, Paper
8. Stochastic stability in three-player games,
(with D. Kamiński and M. Zaborowski) Bull. Math. Biol. 67: 1195-1205 (2005).
Abstract, Paper
9. Population dynamics with a stable efficient equilibrium
(with T. Płatkowski) J. Theor. Biol. 237: 363-368 (2005).
Abstract, Paper
10. Equilibrium transitions in finite populations of players,
Banach Center Publications, Game Theory and Mathematical Economics 71: 237-242 (2006).
Abstract, Paper
Ion channels
1. Jan Gomułkiewicz, Jacek Miękisz i Stanisław Miękisz,
Transport jonów przez nano-kanały w błonach komórkowych
Abstract, Paper
General statistical mechanics
1. Relaxation of the Ferrofluid in a Magnetic Field:
the Cubic Crystal Case. Acta Physica Polonica A57: 623-625 (1980).
2. The Decomposition Property and Equilibrium States of
Ferromagnetic Lattice Systems. Commun. Math. Phys. 109:
353-367 (1987).
3. The Third Law of Thermodynamics (with Charles Radin).
Mod. Phys. Lett. B1: 61-65 (1987).
4. Low Temperature Equilibrium States of Ferromagnetic Lattice
Systems. J. Phys. A.: Math. Gen. 21: 1679-1688 (1988).
5. Frustration without Competing Interactions.
J. Stat. Phys. 55: 351-355 (1989).
Microscopic models of quasicrystals
1. Many Phases in Systems without Periodic Ground States.
Commun. Math. Phys. 107, 577-586, (1986).
2. The Unstable Chemical Structure of Quasicrystalline Alloys
(with Charles Radin). Phys. Lett. 119A: 133-134 (1986).
3. Classical Lattice Gas Model with a Unique Nondegenerate
but Unstable Periodic Ground State Configuration.
Commun. Math. Phys. 111: 533-538 (1987).
4. How Low Temperature Causes Long Range Order.
J. Phys. A.: Math. Gen. 21: L529-L531 (1988).
5. Nonperiodic Order in Classical Lattice Systems.
Nuclear Physics B (Proc. Suppl.) 5A: 122-124 (1988).
6. Why Solids Are Not Really Crystalline? (with Charles Radin).
Phys. Rev. B. 39: 1950-1952 (1989).
7. Toward a Microscopic Model of a Quasicrystal.
Phys. Lett. 138A: 415-416 (1989).
8. Fractal Symmetry in an Ising Model. (with C. Gardner,
C. Radin and A. van Enter) J. Phys. A.: Math. Gen. 22:
L1019-L1023 (1989).
9. A Microscopic Model with Quasicrystalline Properties.
J. Stat. Phys. 58: 1137-1149 (1990).
10. Breaking of Periodicity at Positive Temperatures.
(with Aernout van Enter) Commun. Math. Phys. 134: 647-651 (1990).
11. How Can One Define a (Weak) Crystal? (with Aernout van Enter)
J. Stat. Phys. 66: 1147-1153 (1992).
12. Low Temperature Stability of Nonperiodic Structures.
Physica A, 185: 151-153 (1992).
13. Overlap Distributions for Deterministic Systems with Many
Pure States. (with A. Hof and A.C.D. van Enter)
J. Phys. A: Math. Gen. 25: L1133-L1137 (1992)
14. A Global Minimum of Energy Is Not Always a Sum of Local
Minima - a Note on Frustration. J. Stat. Phys. 71: 425-434 (1993).
15. Stabilities and Instabilities of Nonperiodic Ground States,
in: M. Fannes, C. Maes, and A. Verbeure eds. On Three Levels,
pp. 253-256, New York, Plenum Press (1994).
16. Frustration in Quasicrystal Growth, in the Proceedings
of the conference Mathematical Physics of Disordered Systems, Sorbonne,
July 25-27 (1994).
17. Low-Temperature Stability of Quasicrystals. Physica A 232:
657-661 (1996)
18. Symmetries of Nonperiodic Ground States, in the Proceedings
of the Workshop on Aperiodic Structures, Kraków, July 1-5 (1996).
19. Stable Quasiperiodic Ground States. J. Stat. Phys. 88: 691-711 (1997)
20. Ultimate Frustration in Classical Lattice-Gas Models.
J. Stat. Phys. 90: 285-300 (1998).
21. Nonperiodic Long-Range Order for Fast Decaying Interactions
at Positive Temperatures. (with A. C. D. van Enter and M. Zahradnik)
J. Stat. Phys. 90: 1441-1447 (1998).
22. A Symmetry Group of a Thue-Morse Quasicrystal (with J-P Gazeau).
J. Phys. A: Math. Gen. 31: L435-L440 (1998).
23. Classical Lattice-Gas Models of Quasicrystals.
J. Stat. Phys. 97: 835-850 (1999).
24. Nonperiodic Gibbs States in Microscopic
Models of Quasicrystals, in Mathematical Results in Statistical Mechanics
(str. 501-508), Proceedings of the Satellite Colloquium STATPHYS 20,
eds. J. Ruiz, S. Miracle Sole, and V. Zagrebnov, World Scientific (1999).
25. Ground States of Lattice Gases with ``Almost'' Convex Repulsive
Interactions (with Janusz Jędrzejewski). J. Stat. Phys. 98, 589-620 (2000).
26. Devil's Staircase for Nonconvex Interactions
(with Janusz Jędrzejewski). Europhysics Letters 50: 307-311 (2000).
27. Ground States of Quasilattice-Gas Models
(with J-P Gazeau and R. Krejcar).
Materials Science and Engineering A 294-296: 421-424 (2000).
Book
Quasicrystals - Microscopic Models of Nonperiodic Structures,
Leuven Notes on Mathematical and Theoretical Physics, Leuven
University Press (1993).