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Forward and backward limits
We start by considering irreducible aperiodic positive recurrent Markov chains, and the proof of the main limit theorem...
Structural properties of a conditioned random walk on the integer lattice with local constraints
We consider a random walk on a one/multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death.
The unreasonable effectiveness of determinantal processes
In 1960, Wigner published an article famously titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
Fluctuations of random convex interfaces
We consider the convex hull of a point set constituted with independent and uniformly distributed points in a smooth convex body K of R^d.
Back and forth between the beta distribution and edge stochastic domination in ERAPs
I will survey recent and less recent results on the phase diagram of Euclidean Random Assignment Problems (ERAPs)...
Random Tessellation Forests
Random forests are a popular class of algorithms used for regression and classification.
Sofic entropy of processes on infinite random trees
This is a joint work with Agnes Backhausz et Balasz Szegedy. We define a natural notion of micro-state entropy...
Propagation of chaos and Poisson Hypothesis for replica mean-field models of intensity-based neural…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions.
A Notion of Entropy for Sparse Marked Graphs and its Applications in Graphical Data Compression
Many modern data sources arising from social networks, biological data, etc. are best viewed...
On the dependence structure of negatively dependent measures
A major breakthrough in the theory of negatively dependent – i.e., repulsive – probability measure...
The bias of fluid approximation: Poisson equation, averaging methods and two-timescale processes
Fluid approximation often provide a good tool to study a stochastic process.