arXiv subjects

Ivan N. Burenev

Publications and source records attributed to Ivan N. Burenev.

9 recordsLinked to original sources

arXiv2026

A first passage problem for a Poisson counting process with a linear moving boundary

The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here we present a unified and pedagogical treatment of two approaches: the direct time-domain approach based on path-decomposition techniques and the Laplace-domain approach based on the Pollaczek-Spitzer formula. Beyond streamlining existing derivations and establishing their consistency, we leverage the complementary nature of the two methods to obtain new exact analytical results. Specifically, we derive an explicit large deviation function for the first-passage time distribution in the subcritical regime and closed-form expressions for the conditional mean first-passage time for arbitrary offset. Despite its simplicity, this first crossing process exhibits non-trivial critical behavior and provides a rare example where all the main results of interest can be derived exactly.

cond-mat.stat-mech↗

arXiv2026

First-passage properties of the jump process with a drift. The general case

We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time random walk, we identify three regimes determined by the drift strength: survival (weak drift), absorption (strong drift), and critical. We derive explicit expressions for exponential decay rates in the survival and absorption regimes, and characterize algebraic decay at the critical point. We also obtain asymptotic behavior of the mean first-passage time, number of jumps, and their variances for processes starting either close to the origin or far from it.

cond-mat.stat-mech↗

arXiv2025

An introduction to large deviations with applications in physics

These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications", held in July 2024 at Les Houches in France. They present the basic definitions and mathematical results that form the theory of large deviations, as well as many simple motivating examples of applications in statistical physics, which serve as a basis for the many other lectures given at the school that covered more specific applications in biophysics, random matrix theory, nonequilibrium systems, geophysics, and the simulation of rare events, among other topics. These notes extend the lectures, which can be accessed online, by presenting exercises and pointer references for further reading.

cond-mat.stat-mech↗

arXiv2025

First-passage properties of the jump process with a drift. Two exactly solvable cases

We investigate the first-passage properties of a jump process with a constant drift, focusing on two key observables: the first-passage time $τ$ and the number of jumps $n$ before the first-passage event. By mapping the problem onto an effective discrete-time random walk, we derive an exact expression for the Laplace transform of the joint distribution of $τ$ and $n$ using the generalized Pollaczek-Spitzer formula. This result is then used to analyze the first-passage properties for two exactly solvable cases: (i) both the inter-jump intervals and jump amplitudes are exponentially distributed, and (ii) the inter-jump intervals are exponentially distributed while all jumps have the same fixed amplitude. We show the existence of two distinct regimes governed by the strength of the drift: (i) a survival regime, where the process remains positive indefinitely with finite probability; (ii) an absorption regime, where the first-passage eventually occurs; and (iii) a critical point at the boundary between these two phases. We characterize the asymptotic behavior of survival probabilities in each regime: they decay exponentially to a constant in the survival regime, vanish exponentially fast in the absorption regime, and exhibit power-law decay at the critical point. Furthermore, in the absorption regime, we derive large deviation forms for the marginal distributions of $τ$ and n. The analytical predictions are validated through extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Importance Sampling for counting statistics in one-dimensional systems

In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on selecting an appropriate biased distribution. While exponential tilt in the observable stands as the conventional choice for various problems, its efficiency in the context of counting statistics may be significantly hindered by the genuine discreteness of the observable. To address this challenge, we propose an alternative strategy which we call importance sampling with the local tilt. We demonstrate the efficiency of the proposed approach through the analysis of three prototypical examples: a set of independent Gaussian random variables, Dyson gas, and Symmetric Simple Exclusion Process (SSEP) with a steplike initial condition.

cond-mat.stat-mech↗

arXiv2024

Thermodynamics of the five-vertex model with scalar-product boundary conditions

We consider the homogeneous five-vertex model on a rectangle domain of the square lattice with so-called scalar-product boundary conditions. Peculiarity of these boundary conditions is that the configurations of the model are in an one-to-one correspondence with the 3D Young diagrams limited by a box of a given size. We address the thermodynamics of the model using a connection of the partition function with the $τ$-function of the sixth Painlevé equation. We compute an expansion of the logarithm of the partition function to the order of a constant in the size of the system. We find that the geometry of the domain is crucial for phase transition phenomena. Two cases need to be considered separately: one is where the region has an asymptotically square shape and the second one is where it is of an arbitrary rectangle, but not square, shape. In the first case there are three regimes, which can be attributed to dominance in the configurations of a ferroelectric order, disorder, and anti-ferroelectric order. In the second case the third regime is absent.

math-ph↗

arXiv2024

Occupation time of a system of Brownian particles on the line with steplike initial condition

We consider a system of non-interacting Brownian particles on the line with steplike initial condition and study the statistics of the occupation time on the positive half-line. We demonstrate that this system exhibits long-lasting memory effects of the initialization. Specifically, we calculate the mean and the variance of the occupation time, demonstrating that the memory effects in the variance are determined by a generalized compressibility (or Fano factor), associated with the initial condition. In the particular case of the uncorrelated uniform initial condition we conduct a detailed study of two probability distributions of the occupation time: annealed (averaged over all possible initial configurations) and quenched (for a typical configuration). We show that at large times both the annealed and the quenched distributions admit large deviation form and we compute analytically the associated rate functions. We verify our analytical predictions via numerical simulations using Importance Sampling Monte-Carlo strategy.

cond-mat.stat-mech↗

arXiv2023

Local time of a system of Brownian particles on the line with steplike initial condition

We consider a system of non-interacting Brownian particles on a line with a step-like initial condition, and we investigate the behavior of the local time at the origin at large times. We compute the mean and the variance of the local time, and we show that the memory effects are governed by the Fano factor associated with the initial condition. For the uniform initial condition, we show that the probability distribution of the local time admits a large deviation form, and we compute the corresponding large deviation functions for the annealed and quenched averaging schemes. The two resulting large deviation functions are very different. Our analytical results are supported by extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2020

Determinant formulas for the five-vertex model

We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box of given size). The partition function of an inhomogeneous model is given in terms of a determinant. For the homogeneous model, it can be given in terms of a Hankel determinant. We also show that in the homogeneous case the partition function is a $τ$-function of the sixth Painlevé equation with respect to the rapidity variable of the weights.

math-ph↗