We discuss statistical properties of phase boundary in the 2D low-temperature Ising ferromagnet in a box with the two-component boundary conditions. We prove the weak convergence in C0;1] of measuresâ€¦ (More)

Let X0 = 0, X1, X2, . . . be an aperiodic random walk generated by a sequence Î¾1, Î¾2, . . . of i.i.d. integer-valued random variables with common distribution p (Â·) having zero mean and finiteâ€¦ (More)

The aim of this note is to discuss statistical properties of the phase separation line in the 2D Ising model. The aymptotical properties of the random process corresponding to the uctuations of theâ€¦ (More)

The aim of this note is to prove the functional central limit theorem for certain random process constructed from a random walk conditioned by xing the value at the right end of its trajectories. Theâ€¦ (More)

The aim of this note is to discuss statistical properties of the phase separation line in the 2D Ising model. The aymptotical properties of the random process corresponding to the fluctuations of theâ€¦ (More)

We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated to the gradient-gradient correlations, called theâ€¦ (More)

We study algebraic and topological properties of the convolution semigroups of probability measures on topological groups and show that a compact Clifford topological semigroup S embeds into theâ€¦ (More)

We discuss extensively some properties of the wave numbers in Bethe's ansatz for the 2D ice model. Based on this, we justify thermodynamic limit, the existence of entropy, and obtain some new resultsâ€¦ (More)