8 papers
On perturbations that preserve the connectivity properties in tree percolations
Mirmukhsin Makhmudov, Ville Suomala
We consider a general bond percolation on an infinite locally finite tree, where the edge retention probabilities are replaced by , where $\{q_n\}_{n\ge…
Effective Intrinsic Ergodicity for renewal-type potentials on S-gap shifts
Farhod Haydarov, Shirali Kadyrov, Mirmukhsin Makhmudov +1
We establish effective intrinsic ergodicity for renewal-type potentials on one-sided \(S\)-gap shifts. Inducing on the one-symbol cylinder \([1]\) reduces the system to a full shif…
Concentration inequalities and Transfer operators for supercritical Dyson models
Mirmukhsin Makhmudov
The present paper extends the results on the ferromagnetic Dyson models from \cites{EFMV2024, JOP2025} to the near-critical and strongly interacting regimes. As part of our main re…
Gibbs Properties of Equilibrium States
Mirmukhsin Makhmudov, Evgeny Verbitskiy
We consider the problem of equivalence of Gibbs states and equilibrium states for continuous potentials on full shift spaces . Sinai, Bowen, Ruelle and others estab…
The Eigenfunctions of the Transfer Operator for the Dyson model in a field
Mirmukhsin Makhmudov
The recent works \cite{EFMV2024} and \cite{JOP2023} have studied the spectral properties of the Dyson model in the absence of an external field. This paper is a continuation of \ci…
On an extension of a theorem by Ruelle to long-range potentials
Aernout C. D. van Enter, Roberto Fernández, Mirmukhsin Makhmudov +1
Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding ei…
Multifractal Formalism from Large Deviations
Mirmukhsin Makhmudov, Evgeny Verbitskiy, Qian Xiao
It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived usin…
Description of the set of strictly regular quadratic bistochastic operators and examples
Mirmukhsin Makhmudov
The present paper focuses on the dynamical systems of the quadratic bistochastic operators (QBO) on the standard simplex. In the paper, we show the character of connection of the d…