Université Paris-Saclay

Ultra slow sub-logarithmic diffusion of a sluggish random walker subject to resetting with memory

Denis Boyer, Satya N. Majumdar

We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|…

Exact Stationary State of a $d$ -dimensional Run-and-Tumble Particle in a Harmonic Potential

Mathis Guéneau, Satya N. Majumdar, Grégory Schehr

We derive the exact nonequilibrium steady state of a run-and-tumble particle (RTP) in $d$ dimensions confined in an isotropic harmonic trap $V (r) = μ r^{2} /2$ , with $r=\|\math…

Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

Sumeja Bureković, Filippo De Luca, Michael E. Cates +1

Phase-separating active systems can display phenomenology that is impossible in equilibrium. The binodal densities are not solely determined by a bulk (effective) free energy, but…

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

Ivan N. Burenev, Michael J. Kearney, Satya N. Majumdar

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 t…

Classification of diffusion processes in dimension $d$ via the Carleman approach with applications to models involving additive, multiplicative or square-root noises

Cecile Monthus

The Carleman approach is well-known in the field of deterministic classical dynamics as a method to replace a finite number $d$ of non-linear differential equations by an infinite-…

Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modeling

Marco Baiesi, Alberto Rosso

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a mode…

Burgers dynamics for Poisson point process initial conditions of the Weibull class

Patrick Valageas

We derive the statistical properties of one-dimensional Burgers dynamics with stochastic initial conditions for the velocity potential defined by a Poisson point process whose inte…

Conservation laws and slow dynamics determine the universality class of interfaces in active matter

Raphaël Maire, Andrea Plati, Frank Smallenburg +1

While equilibrium interfaces display universal large-scale statistics, interfaces in phase-separated active and driven systems are predicted to belong to distinct non-equilibrium u…

Backbone three-point correlation function in the two-dimensional Potts model

Ming Li, Youjin Deng, Jesper Lykke Jacobsen +1

We study the three-point correlation function of the backbone in the two-dimensional $Q$ -state Potts model using the Fortuin--Kasteleyn (FK) representation. The backbone is defined…

cond-mat.stat-mech2025★ 3 cited

A set of master variables for the two-star random graph

Pawat Akara-pipattana, Oleg Evnin

The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control…

Emerging correlations between diffusing particles evolving via simultaneous resetting with memory

Denis Boyer, Satya N. Majumdar

We study the emergence of correlations between $N$ components of the position of a diffusive walker in $N$ dimensions that starts at the origin and resets to previously visited sit…

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

Ivan N. Burenev

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 de…

The Tracy-Widom distribution at large Dyson index

Alain Comtet, Pierre Le Doussal, Naftali R. Smith

We study the Tracy-Widom (TW) distribution $f_{β} (a)$ in the limit of large Dyson index $β \to + \infty$ . This distribution describes the fluctuations of the rescaled largest eigenvalu…

Restoring detailed balance in non-Hermitian Markov processes

Tim Van Wesemael, Gilberto Nakamura, Jan Baetens +3

Stochastic processes out-of-equilibrium often involve asymmetric contributions that break detailed balance and lead to non-monotonic entropy production, limiting thermodynamic inte…

cond-mat.stat-mech2025★ 6 cited

Quenched properties of the Spectral Form Factor

Dimitrios Charamis, Manas Kulkarni, Jorge Kurchan +1

The Spectral Form Factor (SFF) is defined as the modulus squared of the partition function in complex temperature for hermitian matrices and a suitable generalisation has been give…

Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols

Gabriele de Mauro, Marco Biroli, Satya N. Majumdar +1

We consider a one-dimensional gas of $N$ independent Brownian particles subject to simultaneous stochastic resetting, with inter-reset times drawn from a general waiting-time distr…

cond-mat.stat-mech2025★ 12 cited

Hyperuniformity and conservation laws in non-equilibrium systems

Raphaël Maire, Ludivine Chaix

We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equili…

Discontinuity in the distribution of field increments between avalanches in non-abelian random field Blume-Emery-Griffiths model with no passing violation

Aldrin B E, Alberto Rosso, Sumedha

We study the zero-temperature quasi-statically driven dynamics of the random field Blume--Emery--Griffiths model (RFBEGM) as a minimal framework to investigate the consequences of…

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors

Cecile Monthus

The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x, x ~)$ is revisited via the spectral decompositions of the…

cond-mat.stat-mech2025★ 5 cited

Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting

Giuseppe Del Vecchio Del Vecchio, Manas Kulkarni, Satya N. Majumdar +1

We introduce \emph{proxitaxis}, a simple search strategy where the searcher has only information about the distance from the target but not the direction. The strategy consists of…

Dynamically emergent correlations in a Brownian gas with diffusing diffusivity

Nikhil Mesquita, Satya N. Majumdar, Sanjib Sabhapandit

We study a gas of $N$ Brownian particles in the presence of a common stochastic diffusivity $D (t) = B^{2} (t)$ , where $B (t)$ represents a one-dimensional Brownian motion at time $t$ . St…

Non-algebraic first return probability of a stretched random walk near a convex boundary and its effect on adsorption

Daniil Fedotov, Sergei Nechaev

The $N$ -step random walk, elongated in the vicinity of a disc (in 2D) or a sphere (in 3D) of radius $R$ , demonstrates a non-algebraic stretched exponential decay $P_N\sim \exp\left…