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In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. As in the continuous case, one can consider discrete maximal Radon transforms...
In this paper, motivated by the idea from Courtois and Denuit et al.(2006), we derive extremal distribution for the discrete 5-convex stochastic ordering. As applications,We improve lower and upper bo...
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations c...
A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the rela...
We present a new construction related to systems of polynomials which are consistent on a cube. The consistent polynomials underlie the integrability of discrete counterparts of integrable partial dif...
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\"odinger model with saturable on-site nonline...

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