6 papers · 1 filter
Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians
Sohom Bhattacharya
Quantum -local spin glass Hamiltonians are natural quantum analogues of the classical spin glass models. We provide an asymptotic characterization of the maximal energy achievab…
LDP for Tensor Forms
Reihaneh Malekian, Sohom Bhattacharya, Nabarun Deb +1
In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of t…
Gibbs Measures with Multilinear Forms
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized -statistic and with a general base measure. Expressing the asympto…
LDP for Inhomogeneous U-Statistics
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multi…
Spectral Edge in Sparse Random Graphs: Upper and Lower Tail Large Deviations
Bhaswar B. Bhattacharya, Sohom Bhattacharya, Shirshendu Ganguly
In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erdős-Rényi random graph , in t…
Upper Tail For Homomorphism Counts In Constrained Sparse Random Graphs
Sohom Bhattacharya, Amir Dembo
Consider the upper tail probability that the homomorphism count of a fixed graph within a large sparse random graph exceeds its expected value by a fixed factor . Go…