48 citations · 166 across the 25 of their papers we have counts for
23 papers · 1 filter
Hydrodynamic limits for TASEP with space-time discontinuities
Jacob Butt, Nicos Georgiou, Enrico Scalas
We develop a hydrodynamic theory for a height-dependent version of the totally asymmetric simple exclusion process in which the jump rate at a growth site is sampled from a macrosc…
A restless time-fractional multiclass queue
Nicos Georgiou, Enrico Scalas, Vladislav Vysotsky
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index and the service completions…
Queuing models with Mittag-Leffler inter-event times
Jacob Butt, Nicos Georgiou, Enrico Scalas
We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffl…
Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
Elnur Emrah, Nicos Georgiou, Janosch Ortmann
We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the inc…
Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution
Nicos Georgiou, Enrico Scalas
Consider a Markov chain with finite state space and suppose you wish to change time replacing the integer step index with a random counting process . What happens to the…
The TASEP on Galton-Watson trees
Nina Gantert, Nicos Georgiou, Dominik Schmid
We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from…
Continuum and thermodynamic limits for a simple random-exchange model
Bertram Düring, Nicos Georgiou, Sara Merino-Aceituno +1
We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this mo…
A Large deviation principle for last passage times in an asymmetric Bernoulli potential
Federico Ciech, Nicos Georgiou
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invar…
Last passage percolation in an exponential environment with discontinuous rates
Federico Ciech, Nicos Georgiou
We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are o…
Order of the variance in the discrete Hammersley process with boundaries
Federico Ciech, Nicos Georgiou
We discuss the order of the variance on a lattice analogue of the Hammersley process with boundaries, for which the environment on each site has independent, Bernoulli distributed…
Optimality Regions and Fluctuations for Bernoulli Last Passage Models
Nicos Georgiou, Janosch Ortmann
We study the sequence alignment problem and its independent version, the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of…
A stylized model for wealth distribution
Bertram Düring, Nicos Georgiou, Enrico Scalas
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians devel…
Geodesics and the competition interface for the corner growth model
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exac…
Stationary cocycles and Busemann functions for the corner growth model
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of ex…
Solvable non-Markovian dynamic network
Nicos Georgiou, Istvan Z. Kiss, Enrico Scalas
Non-Markovian processes are widespread in natural and human-made systems, yet explicit model- ling and analysis of such systems is underdeveloped. We consider a non-Markovian dynam…
The dimension of the range of a transient random walk
Nicos Georgiou, Davar Khoshnevisan, Kunwoo Kim +1
We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z^d. This endeavor solves a problem of Barlow and Taylor (199…
Stationary cocycles for the corner growth model
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exac…
Semi-discrete semi-linear parabolic SPDEs
Nicos Georgiou, Mathew Joseph, Davar Khoshnevisan +1
Consider an infinite system \[\partial_tu_t(x)=(\mathscr{L}u_t)(x)+ σ\bigl(u_t(x)\bigr)\partial_tB_t(x)\] of interacting Itô diffusions, started at a nonnegative deterministic boun…
Ratios of partition functions for the log-gamma polymer
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen +1
We introduce a random walk in random environment associated to an underlying directed polymer model in dimensions. This walk is the positive temperature counterpart of the co…
Positive and zero temperature polymer models
Nicos Georgiou
We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we pr…
Large deviation rate functions for the partition function in a log-gamma distributed random potential
Nicos Georgiou, Timo Seppäläinen
We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explic…
Soft edge results for longest increasing paths on the planar lattice
Nicos Georgiou
For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increas…
TASEP with Discontinuous Jump Rates
Nicos Georgiou, Rohini Kumar, Timo Seppalainen
We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities.…