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Sergey Bocharov

Publications and source records attributed to Sergey Bocharov.

11 recordsLinked to original sources
arXiv2026

Sample genealogies within a Brownian excursion

In this article, we apply It\^o's excursion theory to find the joint law of minima of a Brownian excursion conditioned to go above level $1$ over the intervals defined by $k$ independent identically distributed (i.i.d.) points of intersection of the excursion with level $a \in (0,1]$. This approach offers an intuitive way to find the joint law of coalescent times of an i.i.d. sample of k particles alive at time $a$ in Aldous' continuum random tree of height $1$. This can be thought of as ``sampling of the limit" of critical Galton-Watson trees conditioned to survive a large time, agreeing with some special cases obtained in [4] and [5] which instead consider ``the limit of sampling" from critical Galton-Watson trees.

math.PR↗
arXiv2024

The longest branches in a non-Markovian phylogenetic tree

Consider a Bellman--Harris-type branching process, in which individuals evolve independently of one another, giving birth after a random time $T$ to a random number $L$ of children. In this article, we study the asymptotic behaviour of the length of the longest branches of this branching process at time $t$, both pendant branches (corresponding to individuals still alive at time $t$) and interior branches (corresponding to individuals dead before time $t$).

math.PR↗
arXiv2023

Long edges in Galton-Watson trees

In this article, we will establish a number of results concerning the limiting behaviour of the longest edges in the genealogical tree generated by a continuous-time Galton-Watson (GW) process. Separately, we consider the large time behaviour of the longest pendant edges, the longest (strictly) interior edges, and the longest of all the edges. These results extend the special case of long pendant edges of birth-death processes established in Bocharov, Harris, Kominek, Mooers, and Steel [1] .

math.PR↗
arXiv2018

Branching Brownian Motion with spatially-homogeneous and point-catalytic branching

We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain time-dependent regions and as a consequence the first-order asymptotic behaviour of the rightmost particle.

math.PR↗
arXiv2016

Limiting Distribution of the Rightmost Particle in Catalytic Branching Brownian Motion

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate $βδ_0(\cdot)$, where $δ_0(\cdot)$ is the Dirac delta function and $β$ is some positive constant. We show that the distribution of the rightmost particle centred about $\fracβ{2}t$ converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [6] for the degenerate case of catalytic branching.

math.PR↗
arXiv2015

A note on the polynomial moments of the partition function in the SK model

We prove a simple identity relating the $k$th moment of the partition function $Z_N(\cdot)$ in the SK model to the $N$th moment of the partition function $Z_k(\cdot)$. As a corollary we find a characterisation of the limit $\lim_{N \to \infty} \frac{1}{N} \log \mathbb{E} Z_N(β)^k$ alternative to the one found previously by Michel Talagrand in \cite{4}.

math.PR↗
arXiv2013

Branching Random Walk in an inhomogeneous breeding potential

We consider a continuous-time branching random walk in the inhomogeneous breeding potential $β|.|^p$, where $β> 0$, $p \geq 0$. We prove that the population almost surely explodes in finite time if $p > 1$ and doesn't explode if $p \leq 1$. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.

math.PR↗
arXiv2013

Branching Brownian Motion with catalytic branching at the origin

We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate β> 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles above λt at time t, for λ> 0. As a corollary, we establish the almost sure asymptotic speed of the rightmost particle. We also prove a Strong Law of Large Numbers for this catalytic branching Brownian motion.

math.PR↗
arXiv2002

Polarized x-ray absorption spectra of CuGeO3 at the Cu and Ge K edges

Polarized x-ray absorption near edge structure (XANES) spectra at both the Cu and the Ge K-edges of CuGeO3 are measured and calculated relying on the real-space multiple-scattering formalism within a one-electron approach. The polarization components are resolved not only in the unit cell coordinate system but also in a local frame attached to the nearest neighborhood of the photoabsorbing Cu atom. In that way, features which resist a particular theoretical description can be identified. We have found that it is the out-of-CuO4-plane p_{z'} component which defies the one-electron calculation based on the muffin-tin potential. For the Ge K-edge XANES, the agreement between the theory and the experiment appears to be better for those polarization components which probe more compact local surroundings than for those which probe regions with lower atomic density. Paper published in Phys. Rev. B 66, 155119 (2002) and available on-line at http://link.aps.org/abstract/PRB/v66/e155119.

cond-mat↗