191 citations · 1.4k across the 72 of their papers we have counts for
42 papers · 1 filter
A renewal approach to configurational entropy in one dimension
P. L. Krapivsky, J. M. Luck
We introduce a novel approach, inspired from the theory of renewal processes, to determine the configurational entropy of ensembles of constrained configurations of particles on th…
Evolution of grammatical forms: some quantitative approaches
Jean-Marc Luck, Anita Mehta
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occas…
Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model
P. L. Krapivsky, J. M. Luck
The Ising chain with kinetic constraints provides many examples of totally irreversible zero-temperature dynamics leading to metastability with an exponentially large number of att…
The Glauber-Ising chain under low-temperature protocols
Claude Godrèche, Jean-Marc Luck
This work is devoted to an in-depth analysis of arbitrary temperature protocols applied to the ferromagnetic Glauber-Ising chain launched from a disordered initial state and evolvi…
Maximum and records of random walks with stochastic resetting
Claude Godrèche, Jean-Marc Luck
We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive s…
Survival probability of random walks and Lévy flights with stochastic resetting
Claude Godrèche, Jean-Marc Luck
We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up…
Record statistics of integrated random walks and the random acceleration process
Claude Godrèche, Jean-Marc Luck
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random accelera…
On sequences of records generated by planar random walks
Claude Godrèche, Jean-Marc Luck
We investigate the statistics of three kinds of records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers of these records gro…
On the coexistence of competing languages
Jean-Marc Luck, Anita Mehta
We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others…
Records for the moving average of a time series
Claude Godrèche, Jean-Marc Luck
We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width of a sequence of independent, identically distribute…
Parrondo games as disordered systems
J. M. Luck
Parrondo's paradox refers to the counter-intuitive situation where a winning strategy results from a suitable combination of losing ones. Simple stochastic games exhibiting this pa…
Coverage fluctuations in theater models
P. L. Krapivsky, J. M. Luck
We introduce the theater model, which is the simplest variant of directed random sequential adsorption in one dimension with point source and steric interactions. Particles enter s…
Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
Claude Godrèche, Jean-Marc Luck
We characterise the nonequilibrium stationary state of a generic multivariate Ornstein-Uhlenbeck process involving degrees of freedom. The irreversibility of the process is enc…
Generic phase coexistence in the totally asymmetric kinetic Ising model
Claude Godrèche, Jean-Marc Luck
The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynam…
On an imaginary exponential functional of Brownian motion
D. Gredat, I. Dornic, J. M. Luck
We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary ann…
On leaders and condensates in a growing network
C. Godreche, J. M. Luck
The Bianconi-Barabasi model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fit…
The effects of grain shape and frustration in a granular column near jamming
J. M. Luck, A. Mehta
We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fiel…
The various facets of random walk entropy
Z. Burda, J. Duda, J. M. Luck +1
We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining…
A record-driven growth process
C. Godreche, J. M. Luck
We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime.…
Statistics of quantum transmission in one dimension with broad disorder
D. Boose, J. M. Luck
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by it…
Structure of the stationary state of the asymmetric target process
J. M. Luck, C. Godreche
We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a part…
Dynamical diversity and metastability in a hindered granular column near jamming
J. M. Luck, Anita Mehta
Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investig…
Ground-state structure and dynamics in a toy model for granular compaction
J. M. Luck
We report on a toy model for the glassy compaction dynamics of granular systems, introduced and investigated in collaboration with Anita Mehta and Peter Stadler. A stochastic dynam…
Dynamics of the condensate in zero-range processes
C. Godreche, J. M. Luck
For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especi…