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8 papers · 2 filters
Cutoff for the East process
Shirshendu Ganguly, Eyal Lubetzky, Fabio Martinelli
The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap…
Limit Theorems for Empirical Density of Greatest Common Divisors
Behzad Mehrdad, Lingjiong Zhu
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In thi…
Recurrence and Density Decay for Diffusion-Limited Annihilating Systems
Manuel Cabezas, Leonardo T. Rolla, Vladas Sidoravicius
We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is…
On the largest component in the subcritical regime of the Bohman-Frieze process
Sanchayan Sen
Kang, Perkins and Spencer showed that the size of the largest component of the Bohman-Frieze process at a fixed time smaller than , the critical time for the process is $L…
Strong noise sensitivity and random graphs
Eyal Lubetzky, Jeffrey E. Steif
The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm…
On the probability density function of baskets
Christian Bayer, Peter Friz, Peter Laurence
The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of log…