Clément Cosco

activity

20172025

most citedRenormalizing the Kardar-Parisi-Zhang equation in

d \geq 3

in weak disorder

27 citations · 86 across the 17 of their papers we have counts for

collaborators

18 papers

math.PR2025

A central limit theorem for two-dimensional directed polymers with critical spatial correlation

Clément Cosco, Francesca Cottini, Anna Donadini

On the 1+2 dimensional lattice, we consider a directed polymer in a random Gaussian environment that is independent in time and correlated in space. The spatial correlation is supp…

math.PR2025

The maximum of the two dimensional Gaussian directed polymer in the subcritical regime

Clément Cosco, Shuta Nakajima, Ofer Zeitouni

We study the maximum $ϕ_{N}^{*}$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $N \times N$ box. We show that $ϕ_N^*/\log…

math.PR2025

High moments of 2d directed polymers up to quasi-criticality

Clément Cosco, Shuta Nakajima

We consider two-dimensional directed polymers in random environment in the sub-critical regime and in the quasi-critical regime introduced recently by Caravenna, Cottini and Rossi,…

math.PR2024

On the Central Limit Theorem for the log-partition function of 2D directed polymers

Clément Cosco, Anna Donadini

The log-partition function $lo g W_{N} (β)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when consideri…

math.PR2023

Moments of partition functions of 2D Gaussian polymers in the weak disorder regime -- II

Clément Cosco, Ofer Zeitouni

Let $W_{N} (β) = E_{0} [e^{\sum_{n = 1}^{N} β ω (n, S_{n}) - N β^{2} /2}]$ be the partition function of a two-dimensional directed polymer in a random environment, where $ω(i,x),…

math.PR2021★ 1 cited

Moments of partition functions of 2D Gaussian polymers in the weak disorder regime -- I

Clément Cosco, Ofer Zeitouni

Let $W_{N} (β) = E_{0} [e^{\sum_{n = 1}^{N} β ω (n, S_{n}) - N β^{2} /2}]$ be the partition function of a two-dimensional directed polymer in a random environment, where $ω(i,x),…

math.AP2021

Asymptotics of the $p$ -capacity in the critical regime

Clément Cosco, Shuta Nakajima, Florian Schweiger

In this note, we are interested in the asymptotics as $n \to \infty$ of the $p$ -capacity between the origin and the set $n B$ , where $B$ is the boundary of the unit ball of the lattic…

math.PR2021

A variational formula for large deviations in First-passage percolation under tail estimates

Clément Cosco, Shuta Nakajima

Consider first passage percolation with identical and independent weight distributions and first passage time $T$ . In this paper, we study the upper tail large deviations $\m…

math.PR2020★ 7 cited

Directed polymers on infinite graphs

Clement Cosco, Inbar Seroussi, Ofer Zeitouni

We study the directed polymer model for general graphs (beyond $Z^{d}$ ) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disord…

math.PR2020★ 9 cited

Law of large numbers and fluctuations in the sub-critical and $L^{2}$ regions for SHE and KPZ equation in dimension $d \geq 3$

Clément Cosco, Shuta Nakajima, Makoto Nakashima

There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d \geq 3$ as the smoothing parame…

math.PR2020★ 2 cited

Topologically induced metastability in periodic XY chain

Clément Cosco, Assaf Shapira

Non-trivial topological behavior appears in many different contexts in statistical physics, perhaps the most known one being the Kosterlitz-Thouless phase transition in the two dim…

math.PR2019★ 11 cited

Space-time fluctuation of the Kardar-Parisi-Zhang equation in $d \geq 3$ and the Gaussian free field

Francis Comets, Clément Cosco, Chiranjib Mukherjee

We study the solution $h_{ε}$ of the Kardar-Parisi-Zhang (KPZ) equation for $d \geq 3$ : $$ \frac{\partial}{\partial t} h_{\varepsilon} = \frac12 Δh_{\varepsilon} + \bigg[\f…

math.PR2019★ 4 cited

Gaussian fluctuations for the directed polymer partition function for $d \geq 3$ and in the whole $L^{2}$ -region

Clément Cosco, Shuta Nakajima

We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d - 2) /4} (W_{\infty} - W_{n})$ of the normalized partition function…

math.PR2019★ 27 cited

Renormalizing the Kardar-Parisi-Zhang equation in $d \geq 3$ in weak disorder

Francis Comets, Clement Cosco, Chiranjib Mukherjee

We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is sm…

math.PR2018★ 7 cited

Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder

Francis Comets, Clément Cosco, Chiranjib Mukherjee

We consider the stochastic heat equation on $R^{d}$ with multiplicative space-time white noise noise smoothed in space. For $d \geq 3$ and small noise intensity, the solution…

math.PR2018

The Intermediate Disorder Regime for Brownian Directed Polymers in Poisson Environment

Clément Cosco

We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime, which is a crossover regime between the stro…

math.PR2018★ 10 cited

Brownian Polymers in Poissonian Environment: a survey

Francis Comets, Clément Cosco

We consider a space-time continuous directed polymer in random environment. The path is Brownian and the medium is Poissonian. We review many results obtained in the last decade, a…

math.PR2017★ 8 cited

Hausdorff Dimension of the Record Set of a Fractional Brownian Motion

Lucas Benigni, Clément Cosco, Assaf Shapira +1

We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter $H$ equals $H$ .

A central limit theorem for two-dimensional directed polymers with critical spatial correlation

The maximum of the two dimensional Gaussian directed polymer in the subcritical regime

High moments of 2d directed polymers up to quasi-criticality

On the Central Limit Theorem for the log-partition function of 2D directed polymers

Moments of partition functions of 2D Gaussian polymers in the weak disorder regime -- II

Moments of partition functions of 2D Gaussian polymers in the weak disorder regime -- I

Asymptotics of the p-capacity in the critical regime

A variational formula for large deviations in First-passage percolation under tail estimates

Directed polymers on infinite graphs

Law of large numbers and fluctuations in the sub-critical and L2 regions for SHE and KPZ equation in dimension d≥3

Topologically induced metastability in periodic XY chain

Space-time fluctuation of the Kardar-Parisi-Zhang equation in d≥3 and the Gaussian free field

Gaussian fluctuations for the directed polymer partition function for d≥3 and in the whole L2-region

Renormalizing the Kardar-Parisi-Zhang equation in d≥3 in weak disorder

Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder

The Intermediate Disorder Regime for Brownian Directed Polymers in Poisson Environment

Brownian Polymers in Poissonian Environment: a survey

Hausdorff Dimension of the Record Set of a Fractional Brownian Motion

Asymptotics of the $p$ -capacity in the critical regime

Law of large numbers and fluctuations in the sub-critical and $L^{2}$ regions for SHE and KPZ equation in dimension $d \geq 3$

Space-time fluctuation of the Kardar-Parisi-Zhang equation in $d \geq 3$ and the Gaussian free field

Gaussian fluctuations for the directed polymer partition function for $d \geq 3$ and in the whole $L^{2}$ -region

Renormalizing the Kardar-Parisi-Zhang equation in $d \geq 3$ in weak disorder