Proof of Aldous' spectral gap conjecture (2009)
Caputo, Pietro, Liggett, Thomas M., Richthammer, Thomas
Aldous' spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a...
Convergence to equilibrium of biased plane partitions (2009)
Caputo, Pietro, Martinelli, Fabio, Toninelli, Fabio Lucio
We study a single-flip dynamics for the monotone surface in (2+1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non-intersecting simple paths. When the...
Spectrum of large random reversible Markov chains: heavy tailed weights on the complete graph (2009)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K obtained by assigning i.i.d. non negative weights to the edges of the complete graph over n vertices, and normalizing by the corresponding row sum....
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Spectrum of large random reversible Markov chains: two examples (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior...
Analysis of Top-Swap Shuffling for Genome Rearrangements (2008)
Nayantara Bhatnagar, Pietro Caputo, Prasad Tetali, Eric Vigoda
Abstract: We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating...
Circular Law Theorem for Random Markov Matrices (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained...
On the spectral gap of the Kac walk and other binary collision processes (2008)
We give a new and elementary computation of the spectral gap of the Kac walk on the N-sphere. The result is obtained as a by-product of a more general observation which allows to reduce the analysis...
On the approach to equilibrium for a polymer with adsorption and repulsion (2008)
Caputo, Pietro; Universita Roma Tre; Caputo@mat.uniroma3.it, Martinelli, Fabio; Universita Roma Tre; Martin@mat.uniroma3.it, Toninelli, Fabio Lucio; ENS Lyon; Fltonine@ens-lyon.fr
We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after L steps. In the pinning model each path has a weight lambdaN, where lambda>0 and N is the number...
Spectrum of large random reversible Markov chains (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both...
Spectrum of large random reversible Markov chains (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both...
Convex Entropy Decay via the Bochner-Bakry-Emery approach (2007)
Caputo, Pietro, Pra, Paolo Dai, Posta, Gustavo
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When...
. Every particle at row h tries to jump to an arbitrary empty site at row h 1 with rate q (2007)
Pietro Caputo, Fabio Martinelli
Abstract. Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diusions on the lattice, we consider an anisotropic simple exclusion process...
Abstract. We prove a uniform Poincare inequality for non{interacting unbounded spin systems with a conservation law, when the single{site potential is a bounded perturbation of a convex function. The...
ASYMMETRIC DIFFUSION AND THE ENERGY GAP ABOVE THE 111 GROUND STATE OF THE QUANTUM XXZ MODEL (2007)
Pietro Caputo, Fabio Martinelli
Abstract. We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an...
ASYMMETRIC DIFFUSION AND THE ENRGY GAP ABOVE THE 111 GROUND STATE OF THE QUANTUM XXZ MODEL (2007)
Pietro Caputo, Fabio Martinelli
Abstract. We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an...
On the approach to equilibrium for a polymer with adsorption and repulsion (2007)
Caputo, Pietro, Martinelli, Fabio, Toninelli, Fabio Lucio
We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after L steps (L an even integer). In the 'pinning model' each path \eta has a weight...
Analysis of Top-Swap Shuffling for Genome Rearrangements (2006)
Nayantara Bhatnagar, Pietro Caputo, Prasad Tetali, Eric Vigoda
Abstract: We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating...
Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models (2003)
Caputo, Pietro, Martinelli, Fabio
Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diffusions on the lattice, we consider an anisotropic simple exclusion process with $N$...
Abstract. We observe that a class of conditional probability measures for unbounded spin systems with convex interactions satisfies Poincar'e and logarithmic Sobolev inequalities. For the...
Abstract. We observe that a class of conditional probability measures for unbounded spin systems with convex interactions satises Poincare and logarithmic Sobolev inequalities. For the corresponding...
A Note on Wetting Transition for Gradient Fields (1999)
We prove existence of a wetting transition for two types of gradient fields: 1) Continuous SOS models in any dimension and 2) Massless Gaussian model in two dimensions. Combined with a recent result...
Harmonic crystals statistical mechanics and large deviations /
Techn. University, Diss., 2000--Berlin.