Editor in Chief - Anry Nersessian (Institute of Mathematics NAS, Armenia)
Deputy Editor - Rafayel Barkhudaryan (Institute of Mathematics NAS, Armenia)
Managing Editor - Linda Khachatryan (Institute of Mathematics NAS, Armenia)
e-mail: ajm@instmath.sci.am
According to the latest Scimago Journal Rank, Armenian Journal of Mathematics has maintained its position in Q3 with an SJR score of 0.36.
Read more about Armenian Journal of Mathematics has been recognized as a Q3 journal in SJRIn this paper, we study the additivity property of the transition energy in a finite volume. In particular, we show how this property can be applied to solve the well-known problem of finding the conditions under which a given system of probability distributions parameterized by boundary conditions is a system of conditional probabilities for some finite random field (joint probability distribution).
J. Abrahams and J.B. Thomas, A note on the characterization of bivariate densities by conditional densities. Communications in Statistics - Theory and Methods, 13 (1984), no. 3, pp. 395-400.
B.C. Arnold and S.J. Press, Compatible conditional distributions. J. Am. Stat. Assoc., 84 (1989), no. 405, pp. 152-156.
J. Besag, Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc., Ser. B (Methodological), 36 (1974), no. 2, pp. 192-236.
P. Berti, E. Dreassi and P. Rigo, Compatibility results for conditional distributions. J. Multivar. Anal., 125 (2014), pp. 190-203.
H.Y. Chen, Compatibility of conditionally specified models. Statisics and Probability Letters, 80 (2010), pp. 670-677.
R.L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl., 13 (1968), no. 2, pp. 197-224.
S. Dachian and B.S. Nahapetian, Description of specifications by means of probability distributions in small volumes under condition of very week positivity. J. Stat. Phys. 117 (2004), pp. 281-300.
S. Dachian and B.S. Nahapetian, On the relationship of energy and probability in models of classical statistical physics. Markov Processes Relat. Fields, 25 (2019), no. 4, pp. 649-681.
B.M. Gurevich, On joint distribution of random variables with given cross conditional distributions: Discrete case. Theory Probab. Appl., 36 (1992), no. 2, pp. 371-375.
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6 (1984), no. 6, pp. 721-741.
D. Griffeath, Introduction to Random Fields. In: Denumerable Markov Chains. Graduate Texts in Mathematics 40. Springer, New York, NY, 1976.
L.A. Khachatryan, Gibbsian description of Gaussian random fields. Armen. J. Math., 17 (2025), no. 13, pp. 1-20.
L.A. Khachatryan and B.S. Nahapetian, On the characterization of a finite random field by conditional distribution and its Gibbs form. J. Theor. Probab., 36 (2023), pp. 1743-1761.
L.A. Khachatryan and B.S. Nahapetian, Duality of energy and probability in finite-volume models of statistical physics. Reports of NAS RA, 123 (2023), no. 3-4, pp. 7-14.
L.A. Khachatryan and B.S. Nahapetian, Transition energy field and correlation equations. Reports of NAS RA, 125 (2025), no. 1, pp. 7-14.
L.A. Khachatryan and B.S. Nahapetian, Transition energy fields in the method of correlation equations. J. Contemp. Mathemat. Anal., 60 (2025), no. 4, pp. 354-364.
L.A. Khachatryan and B.S. Nahapetian, Gibbs scheme in the theory of random fields. Ann. Henri Poincare, 27 (2026), pp. 2341-2367.
L.A. Khachatryan and B.S. Nahapetian, Cluster property for generalized correlation functions of spin systems. Markov Processes Relat. Fields, 32 (2026), no. 1, pp. 79-105.
G. Winkler, Image analysis, random fields and dynamic Monte Carlo methods. A mathematical introduction. Berlin; New York: Springer-Verlag, 1995.
Armenian Journal of Mathematics (Armen.J.Math.) aims to publish original research papers and survey articles in all areas of mathematics, enhance the interests, talents, and achievements of all individuals in theoretical mathematics and its applications.
Armen.J.Math. accepts also review articles, short communications, conference proceedings, algorithms, PhD and doctoral theses and other items with a detailed exposition of results, proofs, numerical experiments and examples. One of the purposes is to reflect the progress of the mathematical research in Armenia and, by providing an international forum, to stimulate its further developments.
Armen.J.Math. takes advantage of the World Wide Web as a publication medium for materials containing dynamic, full-color graphics; internal and external hyperlinks to related resources; and other Web-based features.
Papers will be presented on the internet immediately after they are accepted for publication. Full-text access to all papers is available for free so as to reach the widest possible audiences.
Armen.J.Math. welcomes contributors, referees, and readers from all countries.
