What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Algebra
Stanislav Molchanov mainly focuses on Mathematical analysis, Intermittency, Mathematical physics, Random field and Statistical physics. Stanislav Molchanov combines subjects such as Gaussian, Probability theory and Anderson localization with his study of Mathematical analysis. His Intermittency research is multidisciplinary, relying on both Cauchy problem, Initial value problem, Hamiltonian and Partial differential equation.
His Mathematical physics research incorporates elements of Spectrum and Eigenfunction. His study in Eigenfunction is interdisciplinary in nature, drawing from both Matrix, Self-adjoint operator and Resolvent. His Random field research is multidisciplinary, incorporating elements of Random variable and Nonlinear system.
His most cited work include:
- Localization at large disorder and at extreme energies: an elementary derivation (571 citations)
- Parabolic Anderson Problem and Intermittency (287 citations)
- DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY (210 citations)
What are the main themes of his work throughout his whole career to date?
His primary scientific interests are in Mathematical analysis, Statistical physics, Random walk, Mathematical physics and Combinatorics. His work deals with themes such as Eigenvalues and eigenvectors, Lyapunov exponent and Spectrum, which intersect with Mathematical analysis. His Eigenvalues and eigenvectors research incorporates themes from Fractal and Pure mathematics.
His Statistical physics study combines topics from a wide range of disciplines, such as Branching random walk, Lattice, Limit and Intermittency. His Mathematical physics research includes themes of Hamiltonian and Eigenfunction. His Combinatorics study incorporates themes from Phase transition, Central limit theorem and Probability measure.
He most often published in these fields:
- Mathematical analysis (37.98%)
- Statistical physics (26.36%)
- Random walk (24.42%)
What were the highlights of his more recent work (between 2016-2021)?
- Statistical physics (26.36%)
- Random walk (24.42%)
- Lattice (15.89%)
In recent papers he was focusing on the following fields of study:
Stanislav Molchanov mainly investigates Statistical physics, Random walk, Lattice, Branching random walk and Mathematical analysis. His studies in Statistical physics integrate themes in fields like Function, Law of large numbers, Distribution and Population model. The Random walk study combines topics in areas such as Approximations of π, Jump and Cluster analysis.
His research in Lattice intersects with topics in Time evolution, Lyapunov stability, Pure mathematics and Intermittency. His study on Branching random walk also encompasses disciplines like
- Immigration which connect with Econometrics and Random environment,
- Finite variance which connect with Markov chain. The concepts of his Mathematical analysis study are interwoven with issues in Pseudo-monotone operator and Compact operator.
Between 2016 and 2021, his most popular works were:
- Spectral analysis of non-local Schrödinger operators (10 citations)
- Spectral analysis of non-local Schrödinger operators (10 citations)
- On ground state of some non local Schrödinger operators (10 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Algebra
Stanislav Molchanov spends much of his time researching Random walk, Statistical physics, Lattice, Mathematical analysis and Intermittency. Stanislav Molchanov integrates Random walk and Front propagation in his studies. In his research, Immigration and Population model is intimately related to Branching random walk, which falls under the overarching field of Statistical physics.
Stanislav Molchanov has included themes like Pseudo-monotone operator and Compact operator in his Mathematical analysis study. Branching and Constant rate are fields of study that intersect with his Intermittency research. His work focuses on many connections between Pure mathematics and other disciplines, such as Extension, that overlap with his field of interest in Limit.
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