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All Outputs (24)

Branching random walk in a random time-independent environment (2022)
Journal Article
Chernousova, E., Hryniv, O., & Molchanov, S. (2023). Branching random walk in a random time-independent environment. Mathematical Population Studies, 30(2), 73-94. https://doi.org/10.1080/08898480.2022.2140561

In a lattice population model, particles move randomly from one site to another as independent random walks, split into two offspring, or die. If duplication and mortality rates are equal and take the same value over all lattice sites, the resulting... Read More about Branching random walk in a random time-independent environment.

Phase separation and sharp large deviations (2020)
Conference Proceeding
Hryniv, O., & Wallace, C. (2020). Phase separation and sharp large deviations. In S. Poghosyan, M. Rafler, & S. Roelly (Eds.), Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics (155-164). https://doi.org/10.25932/publishup-45919

Using a refined analysis of phase boundaries, we derive sharp asymptotics of the large deviation probabilities for the total magnetisation of a low-temperature Ising model in two dimensions.

Steady states of lattice population models with immigration (2020)
Journal Article
Chernousova, E., Feng, Y., Hryniv, O., Molchanov, S., & Whitmeyer, J. (2021). Steady states of lattice population models with immigration. Mathematical Population Studies, 28(2), 63-80. https://doi.org/10.1080/08898480.2020.1767411

In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in t... Read More about Steady states of lattice population models with immigration.

Population model with immigration in continuous space (2019)
Journal Article
Chernousova, E., Hryniv, O., & Molchanov, S. (2020). Population model with immigration in continuous space. Mathematical Population Studies, 27(4), 199-215. https://doi.org/10.1080/08898480.2019.1626189

In a population model in continuous space, individuals evolve independently as branching random walks subject to immigration. If the underlying branching mechanism is subcritical, the model has a unique steady state for each value of the immigration... Read More about Population model with immigration in continuous space.

Stochastic Model of Microtubule Dynamics (2017)
Journal Article
Hryniv, O., & Martínez Esteban, A. (2017). Stochastic Model of Microtubule Dynamics. Journal of Statistical Physics, 169(1), 203-222. https://doi.org/10.1007/s10955-017-1855-2

We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end.... Read More about Stochastic Model of Microtubule Dynamics.

Random walk in mixed random environment without uniform ellipticity (2013)
Journal Article
Hryniv, O., Menshikov, M. V., & Wade, A. R. (2013). Random walk in mixed random environment without uniform ellipticity. Proceedings of the Steklov Institute of Mathematics, 282(1), 106-123. https://doi.org/10.1134/s0081543813060102

We study a random walk in random environment on ℤ+. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities d... Read More about Random walk in mixed random environment without uniform ellipticity.

Excursions and path functionals for stochastic processes with asymptotically zero drifts (2013)
Journal Article
Hryniv, O., Menshikov, M. V., & Wade, A. R. (2013). Excursions and path functionals for stochastic processes with asymptotically zero drifts. Stochastic Processes and their Applications, 123(6), 1891-1921. https://doi.org/10.1016/j.spa.2013.02.001

We study discrete-time stochastic processes (Xt) on [0,∞) with asymptotically zero mean drifts. Specifically, we consider the critical (Lamperti-type) situation in which the mean drift at x is about c/x. Our focus is the recurrent case (when c is not... Read More about Excursions and path functionals for stochastic processes with asymptotically zero drifts.

Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips (2012)
Journal Article
Hryniv, O., MacPhee, I. M., Menshikov, M. V., & Wade, A. R. (2012). Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips. Electronic Journal of Probability, 17, Article 59. https://doi.org/10.1214/ejp.v17-2216

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also... Read More about Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips.

Regular phase in a model of microtubule growth (2012)
Journal Article
Hryniv, O. (2012). Regular phase in a model of microtubule growth. Markov processes and related fields, 18(2), 177-200

We study a continuous-time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (g... Read More about Regular phase in a model of microtubule growth.

Long-time behaviour in a model of microtubule growth (2010)
Journal Article
Hryniv, O., & Menshikov, M. (2010). Long-time behaviour in a model of microtubule growth. Advances in Applied Probability, 42(1), 268-291. https://doi.org/10.1239/aap/1269611153

We study a continuous-time stochastic process on strings made of two types of particle, whose dynamics mimic the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (glo... Read More about Long-time behaviour in a model of microtubule growth.

Some rigorous results on semiflexible polymers, I: Free and confined polymers (2009)
Journal Article
Hryniv, O., & Velenik, Y. (2009). Some rigorous results on semiflexible polymers, I: Free and confined polymers. Stochastic Processes and their Applications, 119(10), 3081-3100. https://doi.org/10.1016/j.spa.2009.04.002

We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated with the gradient–gradient correlations, called the persistence length, being of the same order as the polym... Read More about Some rigorous results on semiflexible polymers, I: Free and confined polymers.

Homo- and Hetero-Polymers in the Mean-Field Approximation (2009)
Journal Article
Cranston, M., Hryniv, O., & Molchanov, S. (2009). Homo- and Hetero-Polymers in the Mean-Field Approximation. Markov processes and related fields, 15(2), 205-224

We discuss phase transition and Lyapunov exponents for homopolymers and heteropolymers in the mean-eld approximation.

Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint (2004)
Journal Article
Hryniv, O., & Ioffe, D. (2004). Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint. Markov processes and related fields, 10(1), 1-64

The paper considers the ensemble of self-avoiding paths in $Z^2$ which join the positive vertical axis with the positive horizontal axis, and take value on the first quadrant of the plane. To each such path $\omega$ is associated its length $|\omega|... Read More about Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint.

Surface tension and the Ornstein-Zernike behaviour for the 2D Blume-Capel model (2002)
Journal Article
Hryniv, O., & Kotecký, R. (2002). Surface tension and the Ornstein-Zernike behaviour for the 2D Blume-Capel model. Journal of Statistical Physics, 106(3-4), 431-476. https://doi.org/10.1023/a%3A1013797920029

We prove existence of the surface tension in the low temperature 2D Blume Capel model and verify the Ornstein-Zernike asymptotics of the corresponding finite-volume interface partition function.

Phase transition for the spherical hierarchical model (2002)
Journal Article
Ben Arous, G., Hryniv, O., & Molchanov, S. (2002). Phase transition for the spherical hierarchical model. Markov processes and related fields, 8(4), 565-594

We present the whole spectrum of the limit theorems for the total magnetization in the hierarchical version of the spherical model in dimensions dim > 2.

On local behaviour of the phase separation line in the 2D Ising model (1998)
Journal Article
Hryniv, O. (1998). On local behaviour of the phase separation line in the 2D Ising model. Probability Theory and Related Fields, 110(1), 91-107. https://doi.org/10.1007/s004400050146

The aim of this note is to discuss some statistical properties of the phase separation line in the 2D low-temperature Ising model. We prove the functional central limit theorem for the probability distributions describing fluctuations of the phase bo... Read More about On local behaviour of the phase separation line in the 2D Ising model.